diff --git a/p054_poker.txt b/p054_poker.txt new file mode 100644 index 0000000..9ab0024 --- /dev/null +++ b/p054_poker.txt @@ -0,0 +1,1000 @@ +8C TS KC 9H 4S 7D 2S 5D 3S AC +5C AD 5D AC 9C 7C 5H 8D TD KS +3H 7H 6S KC JS QH TD JC 2D 8S +TH 8H 5C QS TC 9H 4D JC KS JS +7C 5H KC QH JD AS KH 4C AD 4S +5H KS 9C 7D 9H 8D 3S 5D 5C AH +6H 4H 5C 3H 2H 3S QH 5S 6S AS +TD 8C 4H 7C TC KC 4C 3H 7S KS +7C 9C 6D KD 3H 4C QS QC AC KH +JC 6S 5H 2H 2D KD 9D 7C AS JS +AD QH TH 9D 8H TS 6D 3S AS AC +2H 4S 5C 5S TC KC JD 6C TS 3C +QD AS 6H JS 2C 3D 9H KC 4H 8S +KD 8S 9S 7C 2S 3S 6D 6S 4H KC +3C 8C 2D 7D 4D 9S 4S QH 4H JD +8C KC 7S TC 2D TS 8H QD AC 5C +3D KH QD 6C 6S AD AS 8H 2H QS +6S 8D 4C 8S 6C QH TC 6D 7D 9D +2S 8D 8C 4C TS 9S 9D 9C AC 3D +3C QS 2S 4H JH 3D 2D TD 8S 9H +5H QS 8S 6D 3C 8C JD AS 7H 7D +6H TD 9D AS JH 6C QC 9S KD JC +AH 8S QS 4D TH AC TS 3C 3D 5C +5S 4D JS 3D 8H 6C TS 3S AD 8C +6D 7C 5D 5H 3S 5C JC 2H 5S 3D +5H 6H 2S KS 3D 5D JD 7H JS 8H +KH 4H AS JS QS QC TC 6D 7C KS +3D QS TS 2H JS 4D AS 9S JC KD +QD 5H 4D 5D KH 7H 3D JS KD 4H +2C 9H 6H 5C 9D 6C JC 2D TH 9S +7D 6D AS QD JH 4D JS 7C QS 5C +3H KH QD AD 8C 8H 3S TH 9D 5S +AH 9S 4D 9D 8S 4H JS 3C TC 8D +2C KS 5H QD 3S TS 9H AH AD 8S +5C 7H 5D KD 9H 4D 3D 2D KS AD +KS KC 9S 6D 2C QH 9D 9H TS TC +9C 6H 5D QH 4D AD 6D QC JS KH +9S 3H 9D JD 5C 4D 9H AS TC QH +2C 6D JC 9C 3C AD 9S KH 9D 7D +KC 9C 7C JC JS KD 3H AS 3C 7D +QD KH QS 2C 3S 8S 8H 9H 9C JC +QH 8D 3C KC 4C 4H 6D AD 9H 9D +3S KS QS 7H KH 7D 5H 5D JD AD +2H 2C 6H TH TC 7D 8D 4H 8C AS +4S 2H AC QC 3S 6D TH 4D 4C KH +4D TC KS AS 7C 3C 6D 2D 9H 6C +8C TD 5D QS 2C 7H 4C 9C 3H 9H +5H JH TS 7S TD 6H AD QD 8H 8S +5S AD 9C 8C 7C 8D 5H 9D 8S 2S +4H KH KS 9S 2S KC 5S AD 4S 7D +QS 9C QD 6H JS 5D AC 8D 2S AS +KH AC JC 3S 9D 9S 3C 9C 5S JS +AD 3C 3D KS 3S 5C 9C 8C TS 4S +JH 8D 5D 6H KD QS QD 3D 6C KC +8S JD 6C 3S 8C TC QC 3C QH JS +KC JC 8H 2S 9H 9C JH 8S 8C 9S +8S 2H QH 4D QC 9D KC AS TH 3C +8S 6H TH 7C 2H 6S 3C 3H AS 7S +QH 5S JS 4H 5H TS 8H AH AC JC +9D 8H 2S 4S TC JC 3C 7H 3H 5C +3D AD 3C 3S 4C QC AS 5D TH 8C +6S 9D 4C JS KH AH TS JD 8H AD +4C 6S 9D 7S AC 4D 3D 3S TC JD +AD 7H 6H 4H JH KC TD TS 7D 6S +8H JH TC 3S 8D 8C 9S 2C 5C 4D +2C 9D KC QH TH QS JC 9C 4H TS +QS 3C QD 8H KH 4H 8D TD 8S AC +7C 3C TH 5S 8H 8C 9C JD TC KD +QC TC JD TS 8C 3H 6H KD 7C TD +JH QS KS 9C 6D 6S AS 9H KH 6H +2H 4D AH 2D JH 6H TD 5D 4H JD +KD 8C 9S JH QD JS 2C QS 5C 7C +4S TC 7H 8D 2S 6H 7S 9C 7C KC +8C 5D 7H 4S TD QC 8S JS 4H KS +AD 8S JH 6D TD KD 7C 6C 2D 7D +JC 6H 6S JS 4H QH 9H AH 4C 3C +6H 5H AS 7C 7S 3D KH KC 5D 5C +JC 3D TD AS 4D 6D 6S QH JD KS +8C 7S 8S QH 2S JD 5C 7H AH QD +8S 3C 6H 6C 2C 8D TD 7D 4C 4D +5D QH KH 7C 2S 7H JS 6D QC QD +AD 6C 6S 7D TH 6H 2H 8H KH 4H +KS JS KD 5D 2D KH 7D 9C 8C 3D +9C 6D QD 3C KS 3S 7S AH JD 2D +AH QH AS JC 8S 8H 4C KC TH 7D +JC 5H TD 7C 5D KD 4C AD 8H JS +KC 2H AC AH 7D JH KH 5D 7S 6D +9S 5S 9C 6H 8S TD JD 9H 6C AC +7D 8S 6D TS KD 7H AC 5S 7C 5D +AH QC JC 4C TC 8C 2H TS 2C 7D +KD KC 6S 3D 7D 2S 8S 3H 5S 5C +8S 5D 8H 4C 6H KC 3H 7C 5S KD +JH 8C 3D 3C 6C KC TD 7H 7C 4C +JC KC 6H TS QS TD KS 8H 8C 9S +6C 5S 9C QH 7D AH KS KC 9S 2C +4D 4S 8H TD 9C 3S 7D 9D AS TH +6S 7D 3C 6H 5D KD 2C 5C 9D 9C +2H KC 3D AD 3H QD QS 8D JC 4S +8C 3H 9C 7C AD 5D JC 9D JS AS +5D 9H 5C 7H 6S 6C QC JC QD 9S +JC QS JH 2C 6S 9C QC 3D 4S TC +4H 5S 8D 3D 4D 2S KC 2H JS 2C +TD 3S TH KD 4D 7H JH JS KS AC +7S 8C 9S 2D 8S 7D 5C AD 9D AS +8C 7H 2S 6C TH 3H 4C 3S 8H AC +KD 5H JC 8H JD 2D 4H TD JH 5C +3D AS QH KS 7H JD 8S 5S 6D 5H +9S 6S TC QS JC 5C 5D 9C TH 8C +5H 3S JH 9H 2S 2C 6S 7S AS KS +8C QD JC QS TC QC 4H AC KH 6C +TC 5H 7D JH 4H 2H 8D JC KS 4D +5S 9C KH KD 9H 5C TS 3D 7D 2D +5H AS TC 4D 8C 2C TS 9D 3H 8D +6H 8D 2D 9H JD 6C 4S 5H 5S 6D +AD 9C JC 7D 6H 9S 6D JS 9H 3C +AD JH TC QS 4C 5D 9S 7C 9C AH +KD 6H 2H TH 8S QD KS 9D 9H AS +4H 8H 8D 5H 6C AH 5S AS AD 8S +QS 5D 4S 2H TD KS 5H AC 3H JC +9C 7D QD KD AC 6D 5H QH 6H 5S +KC AH QH 2H 7D QS 3H KS 7S JD +6C 8S 3H 6D KS QD 5D 5C 8H TC +9H 4D 4S 6S 9D KH QC 4H 6C JD +TD 2D QH 4S 6H JH KD 3C QD 8C +4S 6H 7C QD 9D AS AH 6S AD 3C +2C KC TH 6H 8D AH 5C 6D 8S 5D +TD TS 7C AD JC QD 9H 3C KC 7H +5D 4D 5S 8H 4H 7D 3H JD KD 2D +JH TD 6H QS 4S KD 5C 8S 7D 8H +AC 3D AS 8C TD 7H KH 5D 6C JD +9D KS 7C 6D QH TC JD KD AS KC +JH 8S 5S 7S 7D AS 2D 3D AD 2H +2H 5D AS 3C QD KC 6H 9H 9S 2C +9D 5D TH 4C JH 3H 8D TC 8H 9H +6H KD 2C TD 2H 6C 9D 2D JS 8C +KD 7S 3C 7C AS QH TS AD 8C 2S +QS 8H 6C JS 4C 9S QC AD TD TS +2H 7C TS TC 8C 3C 9H 2D 6D JC +TC 2H 8D JH KS 6D 3H TD TH 8H +9D TD 9H QC 5D 6C 8H 8C KC TS +2H 8C 3D AH 4D TH TC 7D 8H KC +TS 5C 2D 8C 6S KH AH 5H 6H KC +5S 5D AH TC 4C JD 8D 6H 8C 6C +KC QD 3D 8H 2D JC 9H 4H AD 2S +TD 6S 7D JS KD 4H QS 2S 3S 8C +4C 9H JH TS 3S 4H QC 5S 9S 9C +2C KD 9H JS 9S 3H JC TS 5D AC +AS 2H 5D AD 5H JC 7S TD JS 4C +2D 4S 8H 3D 7D 2C AD KD 9C TS +7H QD JH 5H JS AC 3D TH 4C 8H +6D KH KC QD 5C AD 7C 2D 4H AC +3D 9D TC 8S QD 2C JC 4H JD AH +6C TD 5S TC 8S AH 2C 5D AS AC +TH 7S 3D AS 6C 4C 7H 7D 4H AH +5C 2H KS 6H 7S 4H 5H 3D 3C 7H +3C 9S AC 7S QH 2H 3D 6S 3S 3H +2D 3H AS 2C 6H TC JS 6S 9C 6C +QH KD QD 6D AC 6H KH 2C TS 8C +8H 7D 3S 9H 5D 3H 4S QC 9S 5H +2D 9D 7H 6H 3C 8S 5H 4D 3S 4S +KD 9S 4S TC 7S QC 3S 8S 2H 7H +TC 3D 8C 3H 6C 2H 6H KS KD 4D +KC 3D 9S 3H JS 4S 8H 2D 6C 8S +6H QS 6C TC QD 9H 7D 7C 5H 4D +TD 9D 8D 6S 6C TC 5D TS JS 8H +4H KC JD 9H TC 2C 6S 5H 8H AS +JS 9C 5C 6S 9D JD 8H KC 4C 6D +4D 8D 8S 6C 7C 6H 7H 8H 5C KC +TC 3D JC 6D KS 9S 6H 7S 9C 2C +6C 3S KD 5H TS 7D 9H 9S 6H KH +3D QD 4C 6H TS AC 3S 5C 2H KD +4C AS JS 9S 7C TS 7H 9H JC KS +4H 8C JD 3H 6H AD 9S 4S 5S KS +4C 2C 7D 3D AS 9C 2S QS KC 6C +8S 5H 3D 2S AC 9D 6S 3S 4D TD +QD TH 7S TS 3D AC 7H 6C 5D QC +TC QD AD 9C QS 5C 8D KD 3D 3C +9D 8H AS 3S 7C 8S JD 2D 8D KC +4C TH AC QH JS 8D 7D 7S 9C KH +9D 8D 4C JH 2C 2S QD KD TS 4H +4D 6D 5D 2D JH 3S 8S 3H TC KH +AD 4D 2C QS 8C KD JH JD AH 5C +5C 6C 5H 2H JH 4H KS 7C TC 3H +3C 4C QC 5D JH 9C QD KH 8D TC +3H 9C JS 7H QH AS 7C 9H 5H JC +2D 5S QD 4S 3C KC 6S 6C 5C 4C +5D KH 2D TS 8S 9C AS 9S 7C 4C +7C AH 8C 8D 5S KD QH QS JH 2C +8C 9D AH 2H AC QC 5S 8H 7H 2C +QD 9H 5S QS QC 9C 5H JC TH 4H +6C 6S 3H 5H 3S 6H KS 8D AC 7S +AC QH 7H 8C 4S KC 6C 3D 3S TC +9D 3D JS TH AC 5H 3H 8S 3S TC +QD KH JS KS 9S QC 8D AH 3C AC +5H 6C KH 3S 9S JH 2D QD AS 8C +6C 4D 7S 7H 5S JC 6S 9H 4H JH +AH 5S 6H 9S AD 3S TH 2H 9D 8C +4C 8D 9H 7C QC AD 4S 9C KC 5S +9D 6H 4D TC 4C JH 2S 5D 3S AS +2H 6C 7C KH 5C AD QS TH JD 8S +3S 4S 7S AH AS KC JS 2S AD TH +JS KC 2S 7D 8C 5C 9C TS 5H 9D +7S 9S 4D TD JH JS KH 6H 5D 2C +JD JS JC TH 2D 3D QD 8C AC 5H +7S KH 5S 9D 5D TD 4S 6H 3C 2D +4S 5D AC 8D 4D 7C AD AS AH 9C +6S TH TS KS 2C QC AH AS 3C 4S +2H 8C 3S JC 5C 7C 3H 3C KH JH +7S 3H JC 5S 6H 4C 2S 4D KC 7H +4D 7C 4H 9S 8S 6S AD TC 6C JC +KH QS 3S TC 4C 8H 8S AC 3C TS +QD QS TH 3C TS 7H 7D AH TD JC +TD JD QC 4D 9S 7S TS AD 7D AC +AH 7H 4S 6D 7C 2H 9D KS JC TD +7C AH JD 4H 6D QS TS 2H 2C 5C +TC KC 8C 9S 4C JS 3C JC 6S AH +AS 7D QC 3D 5S JC JD 9D TD KH +TH 3C 2S 6H AH AC 5H 5C 7S 8H +QC 2D AC QD 2S 3S JD QS 6S 8H +KC 4H 3C 9D JS 6H 3S 8S AS 8C +7H KC 7D JD 2H JC QH 5S 3H QS +9H TD 3S 8H 7S AC 5C 6C AH 7C +8D 9H AH JD TD QS 7D 3S 9C 8S +AH QH 3C JD KC 4S 5S 5D TD KS +9H 7H 6S JH TH 4C 7C AD 5C 2D +7C KD 5S TC 9D 6S 6C 5D 2S TH +KC 9H 8D 5H 7H 4H QC 3D 7C AS +6S 8S QC TD 4S 5C TH QS QD 2S +8S 5H TH QC 9H 6S KC 7D 7C 5C +7H KD AH 4D KH 5C 4S 2D KC QH +6S 2C TD JC AS 4D 6C 8C 4H 5S +JC TC JD 5S 6S 8D AS 9D AD 3S +6D 6H 5D 5S TC 3D 7D QS 9D QD +4S 6C 8S 3S 7S AD KS 2D 7D 7C +KC QH JC AC QD 5D 8D QS 7H 7D +JS AH 8S 5H 3D TD 3H 4S 6C JH +4S QS 7D AS 9H JS KS 6D TC 5C +2D 5C 6H TC 4D QH 3D 9H 8S 6C +6D 7H TC TH 5S JD 5C 9C KS KD +8D TD QH 6S 4S 6C 8S KC 5C TC +5S 3D KS AC 4S 7D QD 4C TH 2S +TS 8H 9S 6S 7S QH 3C AH 7H 8C +4C 8C TS JS QC 3D 7D 5D 7S JH +8S 7S 9D QC AC 7C 6D 2H JH KC +JS KD 3C 6S 4S 7C AH QC KS 5H +KS 6S 4H JD QS TC 8H KC 6H AS +KH 7C TC 6S TD JC 5C 7D AH 3S +3H 4C 4H TC TH 6S 7H 6D 9C QH +7D 5H 4S 8C JS 4D 3D 8S QH KC +3H 6S AD 7H 3S QC 8S 4S 7S JS +3S JD KH TH 6H QS 9C 6C 2D QD +4S QH 4D 5H KC 7D 6D 8D TH 5S +TD AD 6S 7H KD KH 9H 5S KC JC +3H QC AS TS 4S QD KS 9C 7S KC +TS 6S QC 6C TH TC 9D 5C 5D KD +JS 3S 4H KD 4C QD 6D 9S JC 9D +8S JS 6D 4H JH 6H 6S 6C KS KH +AC 7D 5D TC 9S KH 6S QD 6H AS +AS 7H 6D QH 8D TH 2S KH 5C 5H +4C 7C 3D QC TC 4S KH 8C 2D JS +6H 5D 7S 5H 9C 9H JH 8S TH 7H +AS JS 2S QD KH 8H 4S AC 8D 8S +3H 4C TD KD 8C JC 5C QS 2D JD +TS 7D 5D 6C 2C QS 2H 3C AH KS +4S 7C 9C 7D JH 6C 5C 8H 9D QD +2S TD 7S 6D 9C 9S QS KH QH 5C +JC 6S 9C QH JH 8D 7S JS KH 2H +8D 5H TH KC 4D 4S 3S 6S 3D QS +2D JD 4C TD 7C 6D TH 7S JC AH +QS 7S 4C TH 9D TS AD 4D 3H 6H +2D 3H 7D JD 3D AS 2S 9C QC 8S +4H 9H 9C 2C 7S JH KD 5C 5D 6H +TC 9H 8H JC 3C 9S 8D KS AD KC +TS 5H JD QS QH QC 8D 5D KH AH +5D AS 8S 6S 4C AH QC QD TH 7H +3H 4H 7D 6S 4S 9H AS 8H JS 9D +JD 8C 2C 9D 7D 5H 5S 9S JC KD +KD 9C 4S QD AH 7C AD 9D AC TD +6S 4H 4S 9C 8D KS TC 9D JH 7C +5S JC 5H 4S QH AC 2C JS 2S 9S +8C 5H AS QD AD 5C 7D 8S QC TD +JC 4C 8D 5C KH QS 4D 6H 2H 2C +TH 4S 2D KC 3H QD AC 7H AD 9D +KH QD AS 8H TH KC 8D 7S QH 8C +JC 6C 7D 8C KH AD QS 2H 6S 2D +JC KH 2D 7D JS QC 5H 4C 5D AD +TS 3S AD 4S TD 2D TH 6S 9H JH +9H 2D QS 2C 4S 3D KH AS AC 9D +KH 6S 8H 4S KD 7D 9D TS QD QC +JH 5H AH KS AS AD JC QC 5S KH +5D 7D 6D KS KD 3D 7C 4D JD 3S +AC JS 8D 5H 9C 3H 4H 4D TS 2C +6H KS KH 9D 7C 2S 6S 8S 2H 3D +6H AC JS 7S 3S TD 8H 3H 4H TH +9H TC QC KC 5C KS 6H 4H AC 8S +TC 7D QH 4S JC TS 6D 6C AC KH +QH 7D 7C JH QS QD TH 3H 5D KS +3D 5S 8D JS 4C 2C KS 7H 9C 4H +5H 8S 4H TD 2C 3S QD QC 3H KC +QC JS KD 9C AD 5S 9D 7D 7H TS +8C JC KH 7C 7S 6C TS 2C QD TH +5S 9D TH 3C 7S QH 8S 9C 2H 5H +5D 9H 6H 2S JS KH 3H 7C 2H 5S +JD 5D 5S 2C TC 2S 6S 6C 3C 8S +4D KH 8H 4H 2D KS 3H 5C 2S 9H +3S 2D TD 7H 8S 6H JD KC 9C 8D +6S QD JH 7C 9H 5H 8S 8H TH TD +QS 7S TD 7D TS JC KD 7C 3C 2C +3C JD 8S 4H 2D 2S TD AS 4D AC +AH KS 6C 4C 4S 7D 8C 9H 6H AS +5S 3C 9S 2C QS KD 4D 4S AC 5D +2D TS 2C JS KH QH 5D 8C AS KC +KD 3H 6C TH 8S 7S KH 6H 9S AC +6H 7S 6C QS AH 2S 2H 4H 5D 5H +5H JC QD 2C 2S JD AS QC 6S 7D +6C TC AS KD 8H 9D 2C 7D JH 9S +2H 4C 6C AH 8S TD 3H TH 7C TS +KD 4S TS 6C QH 8D 9D 9C AH 7D +6D JS 5C QD QC 9C 5D 8C 2H KD +3C QH JH AD 6S AH KC 8S 6D 6H +3D 7C 4C 7S 5S 3S 6S 5H JC 3C +QH 7C 5H 3C 3S 8C TS 4C KD 9C +QD 3S 7S 5H 7H QH JC 7C 8C KD +3C KD KH 2S 4C TS AC 6S 2C 7C +2C KH 3C 4C 6H 4D 5H 5S 7S QD +4D 7C 8S QD TS 9D KS 6H KD 3C +QS 4D TS 7S 4C 3H QD 8D 9S TC +TS QH AC 6S 3C 9H 9D QS 8S 6H +3S 7S 5D 4S JS 2D 6C QH 6S TH +4C 4H AS JS 5D 3D TS 9C AC 8S +6S 9C 7C 3S 5C QS AD AS 6H 3C +9S 8C 7H 3H 6S 7C AS 9H JD KH +3D 3H 7S 4D 6C 7C AC 2H 9C TH +4H 5S 3H AC TC TH 9C 9H 9S 8D +8D 9H 5H 4D 6C 2H QD 6S 5D 3S +4C 5C JD QS 4D 3H TH AC QH 8C +QC 5S 3C 7H AD 4C KS 4H JD 6D +QS AH 3H KS 9H 2S JS JH 5H 2H +2H 5S TH 6S TS 3S KS 3C 5H JS +2D 9S 7H 3D KC JH 6D 7D JS TD +AC JS 8H 2C 8C JH JC 2D TH 7S +5D 9S 8H 2H 3D TC AH JC KD 9C +9D QD JC 2H 6D KH TS 9S QH TH +2C 8D 4S JD 5H 3H TH TC 9C KC +AS 3D 9H 7D 4D TH KH 2H 7S 3H +4H 7S KS 2S JS TS 8S 2H QD 8D +5S 6H JH KS 8H 2S QC AC 6S 3S +JC AS AD QS 8H 6C KH 4C 4D QD +2S 3D TS TD 9S KS 6S QS 5C 8D +3C 6D 4S QC KC JH QD TH KH AD +9H AH 4D KS 2S 8D JH JC 7C QS +2D 6C TH 3C 8H QD QH 2S 3S KS +6H 5D 9S 4C TS TD JS QD 9D JD +5H 8H KH 8S KS 7C TD AD 4S KD +2C 7C JC 5S AS 6C 7D 8S 5H 9C +6S QD 9S TS KH QS 5S QH 3C KC +7D 3H 3C KD 5C AS JH 7H 6H JD +9D 5C 9H KC 8H KS 4S AD 4D 2S +3S JD QD 8D 2S 7C 5S 6S 5H TS +6D 9S KC TD 3S 6H QD JD 5C 8D +5H 9D TS KD 8D 6H TD QC 4C 7D +6D 4S JD 9D AH 9S AS TD 9H QD +2D 5S 2H 9C 6H 9S TD QC 7D TC +3S 2H KS TS 2C 9C 8S JS 9D 7D +3C KC 6D 5D 6C 6H 8S AS 7S QS +JH 9S 2H 8D 4C 8H 9H AD TH KH +QC AS 2S JS 5C 6H KD 3H 7H 2C +QD 8H 2S 8D 3S 6D AH 2C TC 5C +JD JS TS 8S 3H 5D TD KC JC 6H +6S QS TC 3H 5D AH JC 7C 7D 4H +7C 5D 8H 9C 2H 9H JH KH 5S 2C +9C 7H 6S TH 3S QC QD 4C AC JD +2H 5D 9S 7D KC 3S QS 2D AS KH +2S 4S 2H 7D 5C TD TH QH 9S 4D +6D 3S TS 6H 4H KS 9D 8H 5S 2D +9H KS 4H 3S 5C 5D KH 6H 6S JS +KC AS 8C 4C JC KH QC TH QD AH +6S KH 9S 2C 5H TC 3C 7H JC 4D +JD 4S 6S 5S 8D 7H 7S 4D 4C 2H +7H 9H 5D KH 9C 7C TS TC 7S 5H +4C 8D QC TS 4S 9H 3D AD JS 7C +8C QS 5C 5D 3H JS AH KC 4S 9D +TS JD 8S QS TH JH KH 2D QD JS +JD QC 5D 6S 9H 3S 2C 8H 9S TS +2S 4C AD 7H JC 5C 2D 6D 4H 3D +7S JS 2C 4H 8C AD QD 9C 3S TD +JD TS 4C 6H 9H 7D QD 6D 3C AS +AS 7C 4C 6S 5D 5S 5C JS QC 4S +KD 6S 9S 7C 3C 5S 7D JH QD JS +4S 7S JH 2C 8S 5D 7H 3D QH AD +TD 6H 2H 8D 4H 2D 7C AD KH 5D +TS 3S 5H 2C QD AH 2S 5C KH TD +KC 4D 8C 5D AS 6C 2H 2S 9H 7C +KD JS QC TS QS KH JH 2C 5D AD +3S 5H KC 6C 9H 3H 2H AD 7D 7S +7S JS JH KD 8S 7D 2S 9H 7C 2H +9H 2D 8D QC 6S AD AS 8H 5H 6C +2S 7H 6C 6D 7D 8C 5D 9D JC 3C +7C 9C 7H JD 2H KD 3S KH AD 4S +QH AS 9H 4D JD KS KD TS KH 5H +4C 8H 5S 3S 3D 7D TD AD 7S KC +JS 8S 5S JC 8H TH 9C 4D 5D KC +7C 5S 9C QD 2C QH JS 5H 8D KH +TD 2S KS 3D AD KC 7S TC 3C 5D +4C 2S AD QS 6C 9S QD TH QH 5C +8C AD QS 2D 2S KC JD KS 6C JC +8D 4D JS 2H 5D QD 7S 7D QH TS +6S 7H 3S 8C 8S 9D QS 8H 6C 9S +4S TC 2S 5C QD 4D QS 6D TH 6S +3S 5C 9D 6H 8D 4C 7D TC 7C TD +AH 6S AS 7H 5S KD 3H 5H AC 4C +8D 8S AH KS QS 2C AD 6H 7D 5D +6H 9H 9S 2H QS 8S 9C 5D 2D KD +TS QC 5S JH 7D 7S TH 9S 9H AC +7H 3H 6S KC 4D 6D 5C 4S QD TS +TD 2S 7C QD 3H JH 9D 4H 7S 7H +KS 3D 4H 5H TC 2S AS 2D 6D 7D +8H 3C 7H TD 3H AD KC TH 9C KH +TC 4C 2C 9S 9D 9C 5C 2H JD 3C +3H AC TS 5D AD 8D 6H QC 6S 8C +2S TS 3S JD 7H 8S QH 4C 5S 8D +AC 4S 6C 3C KH 3D 7C 2D 8S 2H +4H 6C 8S TH 2H 4S 8H 9S 3H 7S +7C 4C 9C 2C 5C AS 5D KD 4D QH +9H 4H TS AS 7D 8D 5D 9S 8C 2H +QC KD AC AD 2H 7S AS 3S 2D 9S +2H QC 8H TC 6D QD QS 5D KH 3C +TH JD QS 4C 2S 5S AD 7H 3S AS +7H JS 3D 6C 3S 6D AS 9S AC QS +9C TS AS 8C TC 8S 6H 9D 8D 6C +4D JD 9C KC 7C 6D KS 3S 8C AS +3H 6S TC 8D TS 3S KC 9S 7C AS +8C QC 4H 4S 8S 6C 3S TC AH AC +4D 7D 5C AS 2H 6S TS QC AD TC +QD QC 8S 4S TH 3D AH TS JH 4H +5C 2D 9S 2C 3H 3C 9D QD QH 7D +KC 9H 6C KD 7S 3C 4D AS TC 2D +3D JS 4D 9D KS 7D TH QC 3H 3C +8D 5S 2H 9D 3H 8C 4C 4H 3C TH +JC TH 4S 6S JD 2D 4D 6C 3D 4C +TS 3S 2D 4H AC 2C 6S 2H JH 6H +TD 8S AD TC AH AC JH 9S 6S 7S +6C KC 4S JD 8D 9H 5S 7H QH AH +KD 8D TS JH 5C 5H 3H AD AS JS +2D 4H 3D 6C 8C 7S AD 5D 5C 8S +TD 5D 7S 9C 4S 5H 6C 8C 4C 8S +JS QH 9C AS 5C QS JC 3D QC 7C +JC 9C KH JH QS QC 2C TS 3D AD +5D JH AC 5C 9S TS 4C JD 8C KS +KC AS 2D KH 9H 2C 5S 4D 3D 6H +TH AH 2D 8S JC 3D 8C QH 7S 3S +8H QD 4H JC AS KH KS 3C 9S 6D +9S QH 7D 9C 4S AC 7H KH 4D KD +AH AD TH 6D 9C 9S KD KS QH 4H +QD 6H 9C 7C QS 6D 6S 9D 5S JH +AH 8D 5H QD 2H JC KS 4H KH 5S +5C 2S JS 8D 9C 8C 3D AS KC AH +JD 9S 2H QS 8H 5S 8C TH 5C 4C +QC QS 8C 2S 2C 3S 9C 4C KS KH +2D 5D 8S AH AD TD 2C JS KS 8C +TC 5S 5H 8H QC 9H 6H JD 4H 9S +3C JH 4H 9H AH 4S 2H 4C 8D AC +8S TH 4D 7D 6D QD QS 7S TC 7C +KH 6D 2D JD 5H JS QD JH 4H 4S +9C 7S JH 4S 3S TS QC 8C TC 4H +QH 9D 4D JH QS 3S 2C 7C 6C 2D +4H 9S JD 5C 5H AH 9D TS 2D 4C +KS JH TS 5D 2D AH JS 7H AS 8D +JS AH 8C AD KS 5S 8H 2C 6C TH +2H 5D AD AC KS 3D 8H TS 6H QC +6D 4H TS 9C 5H JS JH 6S JD 4C +JH QH 4H 2C 6D 3C 5D 4C QS KC +6H 4H 6C 7H 6S 2S 8S KH QC 8C +3H 3D 5D KS 4H TD AD 3S 4D TS +5S 7C 8S 7D 2C KS 7S 6C 8C JS +5D 2H 3S 7C 5C QD 5H 6D 9C 9H +JS 2S KD 9S 8D TD TS AC 8C 9D +5H QD 2S AC 8C 9H KS 7C 4S 3C +KH AS 3H 8S 9C JS QS 4S AD 4D +AS 2S TD AD 4D 9H JC 4C 5H QS +5D 7C 4H TC 2D 6C JS 4S KC 3S +4C 2C 5D AC 9H 3D JD 8S QS QH +2C 8S 6H 3C QH 6D TC KD AC AH +QC 6C 3S QS 4S AC 8D 5C AD KH +5S 4C AC KH AS QC 2C 5C 8D 9C +8H JD 3C KH 8D 5C 9C QD QH 9D +7H TS 2C 8C 4S TD JC 9C 5H QH +JS 4S 2C 7C TH 6C AS KS 7S JD +JH 7C 9H 7H TC 5H 3D 6D 5D 4D +2C QD JH 2H 9D 5S 3D TD AD KS +JD QH 3S 4D TH 7D 6S QS KS 4H +TC KS 5S 8D 8H AD 2S 2D 4C JH +5S JH TC 3S 2D QS 9D 4C KD 9S +AC KH 3H AS 9D KC 9H QD 6C 6S +9H 7S 3D 5C 7D KC TD 8H 4H 6S +3C 7H 8H TC QD 4D 7S 6S QH 6C +6D AD 4C QD 6C 5D 7D 9D KS TS +JH 2H JD 9S 7S TS KH 8D 5D 8H +2D 9S 4C 7D 9D 5H QD 6D AC 6S +7S 6D JC QD JH 4C 6S QS 2H 7D +8C TD JH KD 2H 5C QS 2C JS 7S +TC 5H 4H JH QD 3S 5S 5D 8S KH +KS KH 7C 2C 5D JH 6S 9C 6D JC +5H AH JD 9C JS KC 2H 6H 4D 5S +AS 3C TH QC 6H 9C 8S 8C TD 7C +KC 2C QD 9C KH 4D 7S 3C TS 9H +9C QC 2S TS 8C TD 9S QD 3S 3C +4D 9D TH JH AH 6S 2S JD QH JS +QD 9H 6C KD 7D 7H 5D 6S 8H AH +8H 3C 4S 2H 5H QS QH 7S 4H AC +QS 3C 7S 9S 4H 3S AH KS 9D 7C +AD 5S 6S 2H 2D 5H TC 4S 3C 8C +QH TS 6S 4D JS KS JH AS 8S 6D +2C 8S 2S TD 5H AS TC TS 6C KC +KC TS 8H 2H 3H 7C 4C 5S TH TD +KD AD KH 7H 7S 5D 5H 5S 2D 9C +AD 9S 3D 7S 8C QC 7C 9C KD KS +3C QC 9S 8C 4D 5C AS QD 6C 2C +2H KC 8S JD 7S AC 8D 5C 2S 4D +9D QH 3D 2S TC 3S KS 3C 9H TD +KD 6S AC 2C 7H 5H 3S 6C 6H 8C +QH TC 8S 6S KH TH 4H 5D TS 4D +8C JS 4H 6H 2C 2H 7D AC QD 3D +QS KC 6S 2D 5S 4H TD 3H JH 4C +7S 5H 7H 8H KH 6H QS TH KD 7D +5H AD KD 7C KH 5S TD 6D 3C 6C +8C 9C 5H JD 7C KC KH 7H 2H 3S +7S 4H AD 4D 8S QS TH 3D 7H 5S +8D TC KS KD 9S 6D AD JD 5C 2S +7H 8H 6C QD 2H 6H 9D TC 9S 7C +8D 6D 4C 7C 6C 3C TH KH JS JH +5S 3S 8S JS 9H AS AD 8H 7S KD +JH 7C 2C KC 5H AS AD 9C 9S JS +AD AC 2C 6S QD 7C 3H TH KS KD +9D JD 4H 8H 4C KH 7S TS 8C KC +3S 5S 2H 7S 6H 7D KS 5C 6D AD +5S 8C 9H QS 7H 7S 2H 6C 7D TD +QS 5S TD AC 9D KC 3D TC 2D 4D +TD 2H 7D JD QD 4C 7H 5D KC 3D +4C 3H 8S KD QH 5S QC 9H TC 5H +9C QD TH 5H TS 5C 9H AH QH 2C +4D 6S 3C AC 6C 3D 2C 2H TD TH +AC 9C 5D QC 4D AD 8D 6D 8C KC +AD 3C 4H AC 8D 8H 7S 9S TD JC +4H 9H QH JS 2D TH TD TC KD KS +5S 6S 9S 8D TH AS KH 5H 5C 8S +JD 2S 9S 6S 5S 8S 5D 7S 7H 9D +5D 8C 4C 9D AD TS 2C 7D KD TC +8S QS 4D KC 5C 8D 4S KH JD KD +AS 5C AD QH 7D 2H 9S 7H 7C TC +2S 8S JD KH 7S 6C 6D AD 5D QC +9H 6H 3S 8C 8H AH TC 4H JS TD +2C TS 4D 7H 2D QC 9C 5D TH 7C +6C 8H QC 5D TS JH 5C 5H 9H 4S +2D QC 7H AS JS 8S 2H 4C 4H 8D +JS 6S AC KD 3D 3C 4S 7H TH KC +QH KH 6S QS 5S 4H 3C QD 3S 3H +7H AS KH 8C 4H 9C 5S 3D 6S TS +9C 7C 3H 5S QD 2C 3D AD AC 5H +JH TD 2D 4C TS 3H KH AD 3S 7S +AS 4C 5H 4D 6S KD JC 3C 6H 2D +3H 6S 8C 2D TH 4S AH QH AD 5H +7C 2S 9H 7H KC 5C 6D 5S 3H JC +3C TC 9C 4H QD TD JH 6D 9H 5S +7C 6S 5C 5D 6C 4S 7H 9H 6H AH +AD 2H 7D KC 2C 4C 2S 9S 7H 3S +TH 4C 8S 6S 3S AD KS AS JH TD +5C TD 4S 4D AD 6S 5D TC 9C 7D +8H 3S 4D 4S 5S 6H 5C AC 3H 3D +9H 3C AC 4S QS 8S 9D QH 5H 4D +JC 6C 5H TS AC 9C JD 8C 7C QD +8S 8H 9C JD 2D QC QH 6H 3C 8D +KS JS 2H 6H 5H QH QS 3H 7C 6D +TC 3H 4S 7H QC 2H 3S 8C JS KH +AH 8H 5S 4C 9H JD 3H 7S JC AC +3C 2D 4C 5S 6C 4S QS 3S JD 3D +5H 2D TC AH KS 6D 7H AD 8C 6H +6C 7S 3C JD 7C 8H KS KH AH 6D +AH 7D 3H 8H 8S 7H QS 5H 9D 2D +JD AC 4H 7S 8S 9S KS AS 9D QH +7S 2C 8S 5S JH QS JC AH KD 4C +AH 2S 9H 4H 8D TS TD 6H QH JD +4H JC 3H QS 6D 7S 9C 8S 9D 8D +5H TD 4S 9S 4C 8C 8D 7H 3H 3D +QS KH 3S 2C 2S 3C 7S TD 4S QD +7C TD 4D 5S KH AC AS 7H 4C 6C +2S 5H 6D JD 9H QS 8S 2C 2H TD +2S TS 6H 9H 7S 4H JC 4C 5D 5S +2C 5H 7D 4H 3S QH JC JS 6D 8H +4C QH 7C QD 3S AD TH 8S 5S TS +9H TC 2S TD JC 7D 3S 3D TH QH +7D 4C 8S 5C JH 8H 6S 3S KC 3H +JC 3H KH TC QH TH 6H 2C AC 5H +QS 2H 9D 2C AS 6S 6C 2S 8C 8S +9H 7D QC TH 4H KD QS AC 7S 3C +4D JH 6S 5S 8H KS 9S QC 3S AS +JD 2D 6S 7S TC 9H KC 3H 7D KD +2H KH 7C 4D 4S 3H JS QD 7D KC +4C JC AS 9D 3C JS 6C 8H QD 4D +AH JS 3S 6C 4C 3D JH 6D 9C 9H +9H 2D 8C 7H 5S KS 6H 9C 2S TC +6C 8C AD 7H 6H 3D KH AS 5D TH +KS 8C 3S TS 8S 4D 5S 9S 6C 4H +9H 4S 4H 5C 7D KC 2D 2H 9D JH +5C JS TC 9D 9H 5H 7S KH JC 6S +7C 9H 8H 4D JC KH JD 2H TD TC +8H 6C 2H 2C KH 6H 9D QS QH 5H +AC 7D 2S 3D QD JC 2D 8D JD JH +2H JC 2D 7H 2C 3C 8D KD TD 4H +3S 4H 6D 8D TS 3H TD 3D 6H TH +JH JC 3S AC QH 9H 7H 8S QC 2C +7H TD QS 4S 8S 9C 2S 5D 4D 2H +3D TS 3H 2S QC 8H 6H KC JC KS +5D JD 7D TC 8C 6C 9S 3D 8D AC +8H 6H JH 6C 5D 8D 8S 4H AD 2C +9D 4H 2D 2C 3S TS AS TC 3C 5D +4D TH 5H KS QS 6C 4S 2H 3D AD +5C KC 6H 2C 5S 3C 4D 2D 9H 9S +JD 4C 3H TH QH 9H 5S AH 8S AC +7D 9S 6S 2H TD 9C 4H 8H QS 4C +3C 6H 5D 4H 8C 9C KC 6S QD QS +3S 9H KD TC 2D JS 8C 6S 4H 4S +2S 4C 8S QS 6H KH 3H TH 8C 5D +2C KH 5S 3S 7S 7H 6C 9D QD 8D +8H KS AC 2D KH TS 6C JS KC 7H +9C KS 5C TD QC AH 6C 5H 9S 7C +5D 4D 3H 4H 6S 7C 7S AH QD TD +2H 7D QC 6S TC TS AH 7S 9D 3H +TH 5H QD 9S KS 7S 7C 6H 8C TD +TH 2D 4D QC 5C 7D JD AH 9C 4H +4H 3H AH 8D 6H QC QH 9H 2H 2C +2D AD 4C TS 6H 7S TH 4H QS TD +3C KD 2H 3H QS JD TC QC 5D 8H +KS JC QD TH 9S KD 8D 8C 2D 9C +3C QD KD 6D 4D 8D AH AD QC 8S +8H 3S 9D 2S 3H KS 6H 4C 7C KC +TH 9S 5C 3D 7D 6H AC 7S 4D 2C +5C 3D JD 4D 2D 6D 5H 9H 4C KH +AS 7H TD 6C 2H 3D QD KS 4C 4S +JC 3C AC 7C JD JS 8H 9S QC 5D +JD 6S 5S 2H AS 8C 7D 5H JH 3D +8D TC 5S 9S 8S 3H JC 5H 7S AS +5C TD 3D 7D 4H 8D 7H 4D 5D JS +QS 9C KS TD 2S 8S 5C 2H 4H AS +TH 7S 4H 7D 3H JD KD 5D 2S KC +JD 7H 4S 8H 4C JS 6H QH 5S 4H +2C QS 8C 5S 3H QC 2S 6C QD AD +8C 3D JD TC 4H 2H AD 5S AC 2S +5D 2C JS 2D AD 9D 3D 4C 4S JH +8D 5H 5D 6H 7S 4D KS 9D TD JD +3D 6D 9C 2S AS 7D 5S 5C 8H JD +7C 8S 3S 6S 5H JD TC AD 7H 7S +2S 9D TS 4D AC 8D 6C QD JD 3H +9S KH 2C 3C AC 3D 5H 6H 8D 5D +KS 3D 2D 6S AS 4C 2S 7C 7H KH +AC 2H 3S JC 5C QH 4D 2D 5H 7S +TS AS JD 8C 6H JC 8S 5S 2C 5D +7S QH 7H 6C QC 8H 2D 7C JD 2S +2C QD 2S 2H JC 9C 5D 2D JD JH +7C 5C 9C 8S 7D 6D 8D 6C 9S JH +2C AD 6S 5H 3S KS 7S 9D KH 4C +7H 6C 2C 5C TH 9D 8D 3S QC AH +5S KC 6H TC 5H 8S TH 6D 3C AH +9C KD 4H AD TD 9S 4S 7D 6H 5D +7H 5C 5H 6D AS 4C KD KH 4H 9D +3C 2S 5C 6C JD QS 2H 9D 7D 3H +AC 2S 6S 7S JS QD 5C QS 6H AD +5H TH QC 7H TC 3S 7C 6D KC 3D +4H 3D QC 9S 8H 2C 3S JC KS 5C +4S 6S 2C 6H 8S 3S 3D 9H 3H JS +4S 8C 4D 2D 8H 9H 7D 9D AH TS +9S 2C 9H 4C 8D AS 7D 3D 6D 5S +6S 4C 7H 8C 3H 5H JC AH 9D 9C +2S 7C 5S JD 8C 3S 3D 4D 7D 6S +3C KC 4S 5D 7D 3D JD 7H 3H 4H +9C 9H 4H 4D TH 6D QD 8S 9S 7S +2H AC 8S 4S AD 8C 2C AH 7D TC +TS 9H 3C AD KS TC 3D 8C 8H JD +QC 8D 2C 3C 7D 7C JD 9H 9C 6C +AH 6S JS JH 5D AS QC 2C JD TD +9H KD 2H 5D 2D 3S 7D TC AH TS +TD 8H AS 5D AH QC AC 6S TC 5H +KS 4S 7H 4D 8D 9C TC 2H 6H 3H +3H KD 4S QD QH 3D 8H 8C TD 7S +8S JD TC AH JS QS 2D KH KS 4D +3C AD JC KD JS KH 4S TH 9H 2C +QC 5S JS 9S KS AS 7C QD 2S JD +KC 5S QS 3S 2D AC 5D 9H 8H KS +6H 9C TC AD 2C 6D 5S JD 6C 7C +QS KH TD QD 2C 3H 8S 2S QC AH +9D 9H JH TC QH 3C 2S JS 5C 7H +6C 3S 3D 2S 4S QD 2D TH 5D 2C +2D 6H 6D 2S JC QH AS 7H 4H KH +5H 6S KS AD TC TS 7C AC 4S 4H +AD 3C 4H QS 8C 9D KS 2H 2D 4D +4S 9D 6C 6D 9C AC 8D 3H 7H KD +JC AH 6C TS JD 6D AD 3S 5D QD +JC JH JD 3S 7S 8S JS QC 3H 4S +JD TH 5C 2C AD JS 7H 9S 2H 7S +8D 3S JH 4D QC AS JD 2C KC 6H +2C AC 5H KD 5S 7H QD JH AH 2D +JC QH 8D 8S TC 5H 5C AH 8C 6C +3H JS 8S QD JH 3C 4H 6D 5C 3S +6D 4S 4C AH 5H 5S 3H JD 7C 8D +8H AH 2H 3H JS 3C 7D QC 4H KD +6S 2H KD 5H 8H 2D 3C 8S 7S QD +2S 7S KC QC AH TC QS 6D 4C 8D +5S 9H 2C 3S QD 7S 6C 2H 7C 9D +3C 6C 5C 5S JD JC KS 3S 5D TS +7C KS 6S 5S 2S 2D TC 2H 5H QS +AS 7H 6S TS 5H 9S 9D 3C KD 2H +4S JS QS 3S 4H 7C 2S AC 6S 9D +8C JH 2H 5H 7C 5D QH QS KH QC +3S TD 3H 7C KC 8D 5H 8S KH 8C +4H KH JD TS 3C 7H AS QC JS 5S +AH 9D 2C 8D 4D 2D 6H 6C KC 6S +2S 6H 9D 3S 7H 4D KH 8H KD 3D +9C TC AC JH KH 4D JD 5H TD 3S +7S 4H 9D AS 4C 7D QS 9S 2S KH +3S 8D 8S KS 8C JC 5C KH 2H 5D +8S QH 2C 4D KC JS QC 9D AC 6H +8S 8C 7C JS JD 6S 4C 9C AC 4S +QH 5D 2C 7D JC 8S 2D JS JH 4C +JS 4C 7S TS JH KC KH 5H QD 4S +QD 8C 8D 2D 6S TD 9D AC QH 5S +QH QC JS 3D 3C 5C 4H KH 8S 7H +7C 2C 5S JC 8S 3H QC 5D 2H KC +5S 8D KD 6H 4H QD QH 6D AH 3D +7S KS 6C 2S 4D AC QS 5H TS JD +7C 2D TC 5D QS AC JS QC 6C KC +2C KS 4D 3H TS 8S AD 4H 7S 9S +QD 9H QH 5H 4H 4D KH 3S JC AD +4D AC KC 8D 6D 4C 2D KH 2C JD +2C 9H 2D AH 3H 6D 9C 7D TC KS +8C 3H KD 7C 5C 2S 4S 5H AS AH +TH JD 4H KD 3H TC 5C 3S AC KH +6D 7H AH 7S QC 6H 2D TD JD AS +JH 5D 7H TC 9S 7D JC AS 5S KH +2H 8C AD TH 6H QD KD 9H 6S 6C +QH KC 9D 4D 3S JS JH 4H 2C 9H +TC 7H KH 4H JC 7D 9S 3H QS 7S +AD 7D JH 6C 7H 4H 3S 3H 4D QH +JD 2H 5C AS 6C QC 4D 3C TC JH +AC JD 3H 6H 4C JC AD 7D 7H 9H +4H TC TS 2C 8C 6S KS 2H JD 9S +4C 3H QS QC 9S 9H 6D KC 9D 9C +5C AD 8C 2C QH TH QD JC 8D 8H +QC 2C 2S QD 9C 4D 3S 8D JH QS +9D 3S 2C 7S 7C JC TD 3C TC 9H +3C TS 8H 5C 4C 2C 6S 8D 7C 4H +KS 7H 2H TC 4H 2C 3S AS AH QS +8C 2D 2H 2C 4S 4C 6S 7D 5S 3S +TH QC 5D TD 3C QS KD KC KS AS +4D AH KD 9H KS 5C 4C 6H JC 7S +KC 4H 5C QS TC 2H JC 9S AH QH +4S 9H 3H 5H 3C QD 2H QC JH 8H +5D AS 7H 2C 3D JH 6H 4C 6S 7D +9C JD 9H AH JS 8S QH 3H KS 8H +3S AC QC TS 4D AD 3D AH 8S 9H +7H 3H QS 9C 9S 5H JH JS AH AC +8D 3C JD 2H AC 9C 7H 5S 4D 8H +7C JH 9H 6C JS 9S 7H 8C 9D 4H +2D AS 9S 6H 4D JS JH 9H AD QD +6H 7S JH KH AH 7H TD 5S 6S 2C +8H JH 6S 5H 5S 9D TC 4C QC 9S +7D 2C KD 3H 5H AS QD 7H JS 4D +TS QH 6C 8H TH 5H 3C 3H 9C 9D +AD KH JS 5D 3H AS AC 9S 5C KC +2C KH 8C JC QS 6D AH 2D KC TC +9D 3H 2S 7C 4D 6D KH KS 8D 7D +9H 2S TC JH AC QC 3H 5S 3S 8H +3S AS KD 8H 4C 3H 7C JH QH TS +7S 6D 7H 9D JH 4C 3D 3S 6C AS +4S 2H 2C 4C 8S 5H KC 8C QC QD +3H 3S 6C QS QC 2D 6S 5D 2C 9D +2H 8D JH 2S 3H 2D 6C 5C 7S AD +9H JS 5D QH 8S TS 2H 7S 6S AD +6D QC 9S 7H 5H 5C 7D KC JD 4H +QC 5S 9H 9C 4D 6S KS 2S 4C 7C +9H 7C 4H 8D 3S 6H 5C 8H JS 7S +2D 6H JS TD 4H 4D JC TH 5H KC +AC 7C 8D TH 3H 9S 2D 4C KC 4D +KD QS 9C 7S 3D KS AD TS 4C 4H +QH 9C 8H 2S 7D KS 7H 5D KD 4C +9C 2S 2H JC 6S 6C TC QC JH 5C +7S AC 8H KC 8S 6H QS JC 3D 6S +JS 2D JH 8C 4S 6H 8H 6D 5D AD +6H 7D 2S 4H 9H 7C AS AC 8H 5S +3C JS 4S 6D 5H 2S QH 6S 9C 2C +3D 5S 6S 9S 4C QS 8D QD 8S TC +9C 3D AH 9H 5S 2C 7D AD JC 3S +7H TC AS 3C 6S 6D 7S KH KC 9H +3S TC 8H 6S 5H JH 8C 7D AC 2S +QD 9D 9C 3S JC 8C KS 8H 5D 4D +JS AH JD 6D 9D 8C 9H 9S 8H 3H +2D 6S 4C 4D 8S AD 4S TC AH 9H +TS AC QC TH KC 6D 4H 7S 8C 2H +3C QD JS 9D 5S JC AH 2H TS 9H +3H 4D QH 5D 9C 5H 7D 4S JC 3S +8S TH 3H 7C 2H JD JS TS AC 8D +9C 2H TD KC JD 2S 8C 5S AD 2C +3D KD 7C 5H 4D QH QD TC 6H 7D +7H 2C KC 5S KD 6H AH QC 7S QH +6H 5C AC 5H 2C 9C 2D 7C TD 2S +4D 9D AH 3D 7C JD 4H 8C 4C KS +TH 3C JS QH 8H 4C AS 3D QS QC +4D 7S 5H JH 6D 7D 6H JS KH 3C +QD 8S 7D 2H 2C 7C JC 2S 5H 8C +QH 8S 9D TC 2H AD 7C 8D QD 6S +3S 7C AD 9H 2H 9S JD TS 4C 2D +3S AS 4H QC 2C 8H 8S 7S TD TC +JH TH TD 3S 4D 4H 5S 5D QS 2C +8C QD QH TC 6D 4S 9S 9D 4H QC +8C JS 9D 6H JD 3H AD 6S TD QC +KC 8S 3D 7C TD 7D 8D 9H 4S 3S +6C 4S 3D 9D KD TC KC KS AC 5S +7C 6S QH 3D JS KD 6H 6D 2D 8C +JD 2S 5S 4H 8S AC 2D 6S TS 5C +5H 8C 5S 3C 4S 3D 7C 8D AS 3H +AS TS 7C 3H AD 7D JC QS 6C 6H +3S 9S 4C AC QH 5H 5D 9H TS 4H +6C 5C 7H 7S TD AD JD 5S 2H 2S +7D 6C KC 3S JD 8D 8S TS QS KH +8S QS 8D 6C TH AC AH 2C 8H 9S +7H TD KH QH 8S 3D 4D AH JD AS +TS 3D 2H JC 2S JH KH 6C QC JS +KC TH 2D 6H 7S 2S TC 8C 9D QS +3C 9D 6S KH 8H 6D 5D TH 2C 2H +6H TC 7D AD 4D 8S TS 9H TD 7S +JS 6D JD JC 2H AC 6C 3D KH 8D +KH JD 9S 5D 4H 4C 3H 7S QS 5C +4H JD 5D 3S 3C 4D KH QH QS 7S +JD TS 8S QD AH 4C 6H 3S 5S 2C +QS 3D JD AS 8D TH 7C 6S QC KS +7S 2H 8C QC 7H AC 6D 2D TH KH +5S 6C 7H KH 7D AH 8C 5C 7S 3D +3C KD AD 7D 6C 4D KS 2D 8C 4S +7C 8D 5S 2D 2S AH AD 2C 9D TD +3C AD 4S KS JH 7C 5C 8C 9C TH +AS TD 4D 7C JD 8C QH 3C 5H 9S +3H 9C 8S 9S 6S QD KS AH 5H JH +QC 9C 5S 4H 2H TD 7D AS 8C 9D +8C 2C 9D KD TC 7S 3D KH QC 3C +4D AS 4C QS 5S 9D 6S JD QH KS +6D AH 6C 4C 5H TS 9H 7D 3D 5S +QS JD 7C 8D 9C AC 3S 6S 6C KH +8H JH 5D 9S 6D AS 6S 3S QC 7H +QD AD 5C JH 2H AH 4H AS KC 2C +JH 9C 2C 6H 2D JS 5D 9H KC 6D +7D 9D KD TH 3H AS 6S QC 6H AD +JD 4H 7D KC 3H JS 3C TH 3D QS +4C 3H 8C QD 5H 6H AS 8H AD JD +TH 8S KD 5D QC 7D JS 5S 5H TS +7D KC 9D QS 3H 3C 6D TS 7S AH +7C 4H 7H AH QC AC 4D 5D 6D TH +3C 4H 2S KD 8H 5H JH TC 6C JD +4S 8C 3D 4H JS TD 7S JH QS KD +7C QC KD 4D 7H 6S AD TD TC KH +5H 9H KC 3H 4D 3D AD 6S QD 6H +TH 7C 6H TS QH 5S 2C KC TD 6S +7C 4D 5S JD JH 7D AC KD KH 4H +7D 6C 8D 8H 5C JH 8S QD TH JD +8D 7D 6C 7C 9D KD AS 5C QH JH +9S 2C 8C 3C 4C KS JH 2D 8D 4H +7S 6C JH KH 8H 3H 9D 2D AH 6D +4D TC 9C 8D 7H TD KS TH KD 3C +JD 9H 8D QD AS KD 9D 2C 2S 9C +8D 3H 5C 7H KS 5H QH 2D 8C 9H +2D TH 6D QD 6C KC 3H 3S AD 4C +4H 3H JS 9D 3C TC 5H QH QC JC +3D 5C 6H 3S 3C JC 5S 7S 2S QH +AC 5C 8C 4D 5D 4H 2S QD 3C 3H +2C TD AH 9C KD JS 6S QD 4C QC +QS 8C 3S 4H TC JS 3H 7C JC AD +5H 4D 9C KS JC TD 9S TS 8S 9H +QD TS 7D AS AC 2C TD 6H 8H AH +6S AD 8C 4S 9H 8D 9D KH 8S 3C +QS 4D 2D 7S KH JS JC AD 4C 3C +QS 9S 7H KC TD TH 5H JS AC JH +6D AC 2S QS 7C AS KS 6S KH 5S +6D 8H KH 3C QS 2H 5C 9C 9D 6C +JS 2C 4C 6H 7D JC AC QD TD 3H +4H QC 8H JD 4C KD KS 5C KC 7S +6D 2D 3H 2S QD 5S 7H AS TH 6S +AS 6D 8D 2C 8S TD 8H QD JC AH +9C 9H 2D TD QH 2H 5C TC 3D 8H +KC 8S 3D KH 2S TS TC 6S 4D JH +9H 9D QS AC KC 6H 5D 4D 8D AH +9S 5C QS 4H 7C 7D 2H 8S AD JS +3D AC 9S AS 2C 2D 2H 3H JC KH +7H QH KH JD TC KS 5S 8H 4C 8D +2H 7H 3S 2S 5H QS 3C AS 9H KD +AD 3D JD 6H 5S 9C 6D AC 9S 3S +3D 5D 9C 2D AC 4S 2S AD 6C 6S +QC 4C 2D 3H 6S KC QH QD 2H JH +QC 3C 8S 4D 9S 2H 5C 8H QS QD +6D KD 6S 7H 3S KH 2H 5C JC 6C +3S 9S TC 6S 8H 2D AD 7S 8S TS +3C 6H 9C 3H 5C JC 8H QH TD QD +3C JS QD 5D TD 2C KH 9H TH AS +9S TC JD 3D 5C 5H AD QH 9H KC +TC 7H 4H 8H 3H TD 6S AC 7C 2S +QS 9D 5D 3C JC KS 4D 6C JH 2S +9S 6S 3C 7H TS 4C KD 6D 3D 9C +2D 9H AH AC 7H 2S JH 3S 7C QC +QD 9H 3C 2H AC AS 8S KD 8C KH +2D 7S TD TH 6D JD 8D 4D 2H 5S +8S QH KD JD QS JH 4D KC 5H 3S +3C KH QC 6D 8H 3S AH 7D TD 2D +5S 9H QH 4S 6S 6C 6D TS TH 7S +6C 4C 6D QS JS 9C TS 3H 8D 8S +JS 5C 7S AS 2C AH 2H AD 5S TC +KD 6C 9C 9D TS 2S JC 4H 2C QD +QS 9H TC 3H KC KS 4H 3C AD TH +KH 9C 2H KD 9D TC 7S KC JH 2D +7C 3S KC AS 8C 5D 9C 9S QH 3H +2D 8C TD 4C 2H QC 5D TC 2C 7D +KS 4D 6C QH TD KH 5D 7C AD 8D +2S 9S 8S 4C 8C 3D 6H QD 7C 7H +6C 8S QH 5H TS 5C 3C 4S 2S 2H +8S 6S 2H JC 3S 3H 9D 8C 2S 7H +QC 2C 8H 9C AC JD 4C 4H 6S 3S +3H 3S 7D 4C 9S 5H 8H JC 3D TC +QH 2S 2D 9S KD QD 9H AD 6D 9C +8D 2D KS 9S JC 4C JD KC 4S TH +KH TS 6D 4D 5C KD 5H AS 9H AD +QD JS 7C 6D 5D 5C TH 5H QH QS +9D QH KH 5H JH 4C 4D TC TH 6C +KH AS TS 9D KD 9C 7S 4D 8H 5S +KH AS 2S 7D 9D 4C TS TH AH 7C +KS 4D AC 8S 9S 8D TH QH 9D 5C +5D 5C 8C QS TC 4C 3D 3S 2C 8D +9D KS 2D 3C KC 4S 8C KH 6C JC +8H AH 6H 7D 7S QD 3C 4C 6C KC +3H 2C QH 8H AS 7D 4C 8C 4H KC +QD 5S 4H 2C TD AH JH QH 4C 8S +3H QS 5S JS 8H 2S 9H 9C 3S 2C +6H TS 7S JC QD AC TD KC 5S 3H +QH AS QS 7D JC KC 2C 4C 5C 5S +QH 3D AS JS 4H 8D 7H JC 2S 9C +5D 4D 2S 4S 9D 9C 2D QS 8H 7H +6D 7H 3H JS TS AC 2D JH 7C 8S +JH 5H KC 3C TC 5S 9H 4C 8H 9D +8S KC 5H 9H AD KS 9D KH 8D AH +JC 2H 9H KS 6S 3H QC 5H AH 9C +5C KH 5S AD 6C JC 9H QC 9C TD +5S 5D JC QH 2D KS 8H QS 2H TS +JH 5H 5S AH 7H 3C 8S AS TD KH +6H 3D JD 2C 4C KC 7S AH 6C JH +4C KS 9D AD 7S KC 7D 8H 3S 9C +7H 5C 5H 3C 8H QC 3D KH 6D JC +2D 4H 5D 7D QC AD AH 9H QH 8H +KD 8C JS 9D 3S 3C 2H 5D 6D 2S +8S 6S TS 3C 6H 8D 5S 3H TD 6C +KS 3D JH 9C 7C 9S QS 5S 4H 6H +7S 6S TH 4S KC KD 3S JC JH KS +7C 3C 2S 6D QH 2C 7S 5H 8H AH +KC 8D QD 6D KH 5C 7H 9D 3D 9C +6H 2D 8S JS 9S 2S 6D KC 7C TC +KD 9C JH 7H KC 8S 2S 7S 3D 6H +4H 9H 2D 4C 8H 7H 5S 8S 2H 8D +AD 7C 3C 7S 5S 4D 9H 3D JC KH +5D AS 7D 6D 9C JC 4C QH QS KH +KD JD 7D 3D QS QC 8S 6D JS QD +6S 8C 5S QH TH 9H AS AC 2C JD +QC KS QH 7S 3C 4C 5C KC 5D AH +6C 4H 9D AH 2C 3H KD 3D TS 5C +TD 8S QS AS JS 3H KD AC 4H KS +7D 5D TS 9H 4H 4C 9C 2H 8C QC +2C 7D 9H 4D KS 4C QH AD KD JS +QD AD AH KH 9D JS 9H JC KD JD +8S 3C 4S TS 7S 4D 5C 2S 6H 7C +JS 7S 5C KD 6D QH 8S TD 2H 6S +QH 6C TC 6H TD 4C 9D 2H QC 8H +3D TS 4D 2H 6H 6S 2C 7H 8S 6C +9H 9D JD JH 3S AH 2C 6S 3H 8S +2C QS 8C 5S 3H 2S 7D 3C AD 4S +5C QC QH AS TS 4S 6S 4C 5H JS +JH 5C TD 4C 6H JS KD KH QS 4H +TC KH JC 4D 9H 9D 8D KC 3C 8H +2H TC 8S AD 9S 4H TS 7H 2C 5C +4H 2S 6C 5S KS AH 9C 7C 8H KD +TS QH TD QS 3C JH AH 2C 8D 7D +5D KC 3H 5S AC 4S 7H QS 4C 2H +3D 7D QC KH JH 6D 6C TD TH KD +5S 8D TH 6C 9D 7D KH 8C 9S 6D +JD QS 7S QC 2S QH JC 4S KS 8D +7S 5S 9S JD KD 9C JC AD 2D 7C +4S 5H AH JH 9C 5D TD 7C 2D 6S +KC 6C 7H 6S 9C QD 5S 4H KS TD +6S 8D KS 2D TH TD 9H JD TS 3S +KH JS 4H 5D 9D TC TD QC JD TS +QS QD AC AD 4C 6S 2D AS 3H KC +4C 7C 3C TD QS 9C KC AS 8D AD +KC 7H QC 6D 8H 6S 5S AH 7S 8C +3S AD 9H JC 6D JD AS KH 6S JH +AD 3D TS KS 7H JH 2D JS QD AC +9C JD 7C 6D TC 6H 6C JC 3D 3S +QC KC 3S JC KD 2C 8D AH QS TS +AS KD 3D JD 8H 7C 8C 5C QD 6C diff --git a/s052.ipynb b/s052.ipynb new file mode 100644 index 0000000..d245926 --- /dev/null +++ b/s052.ipynb @@ -0,0 +1,316 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Permuted Multiples\n", + "Source: https://projecteuler.net/problem=52" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem Statement\n", + "It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.\n", + "\n", + "Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Planning\n", + "The number that meets these criteria must setart with the digit '1', otherwise a differentn number of digits will appear for 6x. \n", + "\n", + "If all the numbers 100,000 - 200,000 don't yield results, then the numbers 1,000,000 through 2,000,000 need to be tried.\n", + "\n", + "I will use a function that tests if two numbers have the same digits." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Tinkering" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['b', 'c']\n" + ] + } + ], + "source": [ + "a_list=['a','b','c']\n", + "a_list.remove('a')\n", + "\n", + "print(a_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def contains_same_digits(num_1, num_2):\n", + " \"\"\"\n", + " \n", + " \"\"\"\n", + " num_1_digits = []\n", + " num_2_digits = []\n", + " \n", + " # get all digits from num_1\n", + " if num_1 == 0:\n", + " num_1_digits.append(0)\n", + " else:\n", + " while num_1 > 0:\n", + " last_digit = num_1%10\n", + " \n", + " num_1_digits.append(last_digit)\n", + " \n", + " num_1 = int(num_1/10)\n", + " \n", + " # get all digits from num_2\n", + " if num_2 == 0:\n", + " num_2_digits.append(0)\n", + " else:\n", + " while num_2 > 0:\n", + " last_digit = num_2%10\n", + " \n", + " num_2_digits.append(last_digit)\n", + " \n", + " num_2 = int(num_2/10)\n", + " \n", + " # test if each element of num_2 is in num_1, removing the num_1 digit each time\n", + " same_digits = True\n", + " \n", + " for digit in num_2_digits:\n", + " if digit in num_1_digits:\n", + " num_1_digits.remove(digit)\n", + " else:\n", + " same_digits = False\n", + " break\n", + " \n", + " return same_digits" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "contains_same_digits(10234, 32401)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "contains_same_digits(1, 11)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "142857\n", + "Time elapsed: 0.4749751119014507\n" + ] + } + ], + "source": [ + "## solution loop\n", + "import timeit\n", + "\n", + "start=timeit.default_timer()\n", + "###############################\n", + "\n", + "for x in range(100000, int(1000000/6) + 1 + 1):\n", + " if contains_same_digits(x, 2*x) and contains_same_digits(x, 3*x) \\\n", + " and contains_same_digits(x, 4*x) and contains_same_digits(x, 5*x) \\\n", + " and contains_same_digits(x, 6*x):\n", + " \n", + " print(x)\n", + " \n", + "################################\n", + "end = timeit.default_timer()\n", + "print(f\"Time elapsed: {end-start}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[285714, 428571, 571428, 714285, 857142]\n" + ] + } + ], + "source": [ + "## check\n", + "print([142857 * mult for mult in [2, 3, 4, 5, 6]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solution\n", + "142857" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Post-Solution Tinkering\n", + "Are there other solutions greater than the one observed? " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1428570\n", + "1429857\n", + "Time elapsed: 5.359420240293641\n" + ] + } + ], + "source": [ + "## solution loop\n", + "import timeit\n", + "\n", + "start=timeit.default_timer()\n", + "###############################\n", + "\n", + "for x in range(1000000, int(10000000/6) + 1 + 1):\n", + " if contains_same_digits(x, 2*x) and contains_same_digits(x, 3*x) \\\n", + " and contains_same_digits(x, 4*x) and contains_same_digits(x, 5*x) \\\n", + " and contains_same_digits(x, 6*x):\n", + " \n", + " print(x)\n", + " \n", + "################################\n", + "end = timeit.default_timer()\n", + "print(f\"Time elapsed: {end-start}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[2857140, 4285710, 5714280, 7142850, 8571420]\n" + ] + } + ], + "source": [ + "print([1428570 * mult for mult in [2, 3, 4, 5, 6]])" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[2859714, 4289571, 5719428, 7149285, 8579142]\n" + ] + } + ], + "source": [ + "print([1429857 * mult for mult in [2, 3, 4, 5, 6]])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/s053.ipynb b/s053.ipynb new file mode 100644 index 0000000..a9a2b7a --- /dev/null +++ b/s053.ipynb @@ -0,0 +1,235 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Combinatoric Selections\n", + "https://projecteuler.net/problem=53" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem Statement\n", + "There are exactly ten ways of selecting three from five, 12345:\n", + "\n", + "123, 124, 125, 134, 135, 145, 234, 235, 245, and 345\n", + "\n", + "In combinatorics, we use the notation, \n", + "5C3 = 10.\n", + "\n", + "In general, nCr = n!/(r! * (n-r)!)\n", + " \n", + ", where , r<= n , n! = n * (n-1) * (n-2) *...* 1 and 0! = 1.\n", + "\n", + "It is not until n=23, that a value exceeds one-million: 23C10 = 1144066\n", + ".\n", + "\n", + "How many, not necessarily distinct, values of nCr\n", + " for 1 <= n <= 100, are greater than one-million?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Planning\n", + "Write a function that calculates factorial\n", + "\n", + "Write a function that calculates numbers of combinations\n", + "\n", + "Write a function that tests values of n from 23 to 100 that have combination numbers greater than 1,000,000" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "def factorial(n):\n", + " \n", + " product = 1\n", + " \n", + " if n == 0:\n", + " return product\n", + " else:\n", + " for x in range(1, n+1):\n", + " product *= x\n", + " \n", + " return product" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "720" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "factorial(6)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def combinations(n, r):\n", + " \n", + " if r > n or r < 0:\n", + " raise Exception(\"Improper r value\")\n", + " else:\n", + " return int(factorial(n) / factorial(r) / factorial(n-r))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1144066" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "combinations(23, 10)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4\n" + ] + } + ], + "source": [ + "## testing flow of combination counting\n", + "n = 23\n", + "\n", + "num_r_successful = 0 \n", + "over_1000000 = False\n", + "\n", + "for r in range(1, int(n/2)+1):\n", + " if combinations(n, r) > 1000000:\n", + " over_1000000 = True\n", + " break\n", + " \n", + "if over_1000000:\n", + " if n%2== 0: # if n is even\n", + " num_r_successful = 2*( int(n/2) - r ) + 1\n", + " else:\n", + " num_r_successful = 2*( int(n/2) + 1 - r)\n", + "else:\n", + " num_r_successful = 0\n", + " \n", + " \n", + "print(num_r_successful)\n", + "## includes 23C10, 23C11, 23C12, 23C13" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4075\n" + ] + } + ], + "source": [ + "## solution\n", + "num_r_successful_total = 0\n", + "\n", + "for n in range(23, 100+1):\n", + " num_r_successful = 0 \n", + " over_1000000 = False\n", + "\n", + " for r in range(1, int(n/2)+1):\n", + " if combinations(n, r) > 1000000:\n", + " over_1000000 = True\n", + " break\n", + "\n", + " if over_1000000:\n", + " if n%2== 0: # if n is even\n", + " num_r_successful = 2*( int(n/2) - r ) + 1\n", + " else:\n", + " num_r_successful = 2*( int(n/2) + 1 - r)\n", + " else:\n", + " num_r_successful = 0\n", + " \n", + " num_r_successful_total += num_r_successful\n", + " \n", + "print(num_r_successful_total)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solution\n", + "There are 4075 values of nCr greater than 1000000, not necessarily distinct, such that 1<=n<=100, and 0<=r<=n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/s054.ipynb b/s054.ipynb new file mode 100644 index 0000000..68967f8 --- /dev/null +++ b/s054.ipynb @@ -0,0 +1,759 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Poker hands\n", + "Source: https://projecteuler.net/problem=54" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem statement\n", + "In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way:\n", + "\n", + "High Card: Highest value card.\n", + "One Pair: Two cards of the same value.\n", + "Two Pairs: Two different pairs.\n", + "Three of a Kind: Three cards of the same value.\n", + "Straight: All cards are consecutive values.\n", + "Flush: All cards of the same suit.\n", + "Full House: Three of a kind and a pair.\n", + "Four of a Kind: Four cards of the same value.\n", + "Straight Flush: All cards are consecutive values of same suit.\n", + "Royal Flush: Ten, Jack, Queen, King, Ace, in same suit.\n", + "The cards are valued in the order:\n", + "2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace.\n", + "\n", + "If two players have the same ranked hands then the rank made up of the highest value wins; for example, a pair of eights beats a pair of fives (see example 1 below). But if two ranks tie, for example, both players have a pair of queens, then highest cards in each hand are compared (see example 4 below); if the highest cards tie then the next highest cards are compared, and so on.\n", + "\n", + "Consider the following five hands dealt to two players:\n", + "\n", + "Hand\t \tPlayer 1\t \tPlayer 2\t \tWinner\n", + "\n", + "1\t \t5H 5C 6S 7S KD\n", + "Pair of Fives\n", + " \t2C 3S 8S 8D TD\n", + "Pair of Eights\n", + " \tPlayer 2\n", + " \n", + "2\t \t5D 8C 9S JS AC\n", + "Highest card Ace\n", + " \t2C 5C 7D 8S QH\n", + "Highest card Queen\n", + " \tPlayer 1\n", + " \n", + "3\t \t2D 9C AS AH AC\n", + "Three Aces\n", + " \t3D 6D 7D TD QD\n", + "Flush with Diamonds\n", + " \tPlayer 2\n", + " \n", + "4\t \t4D 6S 9H QH QC\n", + "Pair of Queens\n", + "Highest card Nine\n", + " \t3D 6D 7H QD QS\n", + "Pair of Queens\n", + "Highest card Seven\n", + " \tPlayer 1\n", + " \n", + "5\t \t2H 2D 4C 4D 4S\n", + "Full House\n", + "With Three Fours\n", + " \t3C 3D 3S 9S 9D\n", + "Full House\n", + "with Three Threes\n", + " \tPlayer 1\n", + " \n", + "The file, poker.txt, contains one-thousand random hands dealt to two players. Each line of the file contains ten cards (separated by a single space): the first five are Player 1's cards and the last five are Player 2's cards. You can assume that all hands are valid (no invalid characters or repeated cards), each player's hand is in no specific order, and in each hand there is a clear winner.\n", + "\n", + "How many hands does Player 1 win?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Planning\n", + "Create a function that reads in the data from the file and returns pairs of tuples/lists\n", + "\n", + "Create a function that compares two hands\n", + "* Create functions that determine the value of each hand according to each different possible ranks\n", + "* Create a compareto function that compares \n", + " * Inspire by the java `compareTo` function\n", + "* " + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [], + "source": [ + "def card_tuple_from_str(card_str):\n", + " numeric_val = 0\n", + " suite = ''\n", + "\n", + " if card_str[0] == 'T':\n", + " numeric_val = 10\n", + " elif card_str[0] == 'J':\n", + " numeric_val = 11\n", + " elif card_str[0] == 'Q':\n", + " numeric_val = 12\n", + " elif card_str[0] == 'K':\n", + " numeric_val = 13\n", + " elif card_str[0] == 'A':\n", + " numeric_val = 14\n", + " else:\n", + " numeric_val = int(card_str[0])\n", + "\n", + " suite = card_str[1]\n", + "\n", + " card_tuple = ( numeric_val, suite )\n", + "\n", + " return card_tuple" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(11, 'H')" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "card_tuple_from_str('JH')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(4, 'H')" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "card_tuple_from_str('4H')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(14, 'H')" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "card_tuple_from_str('AH')" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def read_hand_string(line):\n", + " \n", + " line_divided = line.split()\n", + " \n", + " hand_1_str = line_divided[0:5]\n", + " hand_1_tups = []\n", + " for card_str in hand_1_str:\n", + " hand_1_tups.append(card_tuple_from_str(card_str))\n", + " \n", + " \n", + " hand_2_str = line_divided[5:10]\n", + " hand_2_tups = []\n", + " for card_str in hand_2_str:\n", + " hand_2_tups.append(card_tuple_from_str(card_str))\n", + " \n", + " return hand_1_tups, hand_2_tups" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "([(5, 'H'), (5, 'C'), (6, 'S'), (7, 'S'), (0, 'D')],\n", + " [(2, 'C'), (3, 'S'), (8, 'S'), (8, 'D'), (0, 'D')])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "read_hand_string('5H 5C 6S 7S KD 2C 3S 8S 8D TD')" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [], + "source": [ + "def high_card(hand_tups):\n", + " return max([tup[0] for tup in hand_tups])\n", + " \n", + "def one_pair(hand_tups):\n", + " numeric_vals = [tup[0] for tup in hand_tups]\n", + " \n", + " highest_pair = 0\n", + " \n", + " for val in numeric_vals:\n", + " if numeric_vals.count(val) >= 2:\n", + " if val > highest_pair:\n", + " highest_pair = val\n", + " \n", + " return highest_pair\n", + " \n", + "def two_pairs(hand_tups):\n", + " numeric_vals = [tup[0] for tup in hand_tups]\n", + " \n", + " pair_count = 0\n", + " \n", + " for val in numeric_vals:\n", + " if numeric_vals.count(val) >= 2:\n", + " \n", + " while val in numeric_vals: # remove all of same value\n", + " numeric_vals.remove(val)\n", + " \n", + " pair_count += 1\n", + " \n", + " if pair_count >= 2:\n", + " return 1\n", + " else:\n", + " return 0\n", + " \n", + "def three_of_a_kind(hand_tups):\n", + " numeric_vals = [tup[0] for tup in hand_tups]\n", + " \n", + " for val in numeric_vals:\n", + " if numeric_vals.count(val) >= 3:\n", + " return val\n", + " \n", + " return 0" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [], + "source": [ + "#teesting\n", + "hand_tups = [(5, 'C'), (5, 'D'), (2, 'H'), (2, 'C'), (2, 'D')]" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "##\n", + "high_card(hand_tups)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "one_pair(hand_tups)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "two_pairs(hand_tups)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "three_of_a_kind(hand_tups)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "hand_tups_2 = [(5, 'C'), (5, 'D'), (5, 'H'), (3, 'C'), (2, 'D')]" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "two_pairs(hand_tups_2)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "def straight(hand_tups):\n", + " numeric_vals = [tup[0] for tup in hand_tups]\n", + " \n", + " bottom_val = min(numeric_vals)\n", + " \n", + " if bottom_val+1 in numeric_vals \\\n", + " and bottom_val+2 in numeric_vals \\\n", + " and bottom_val+3 in numeric_vals \\\n", + " and bottom_val+4 in numeric_vals:\n", + " \n", + " return bottom_val\n", + " \n", + " return 0" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "straight(hand_tups)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "def flush(hand_tups):\n", + " \n", + " suites = [tup[1] for tup in hand_tups]\n", + " \n", + " if suites[0] == suites[1] and suites[1] == suites[2] \\\n", + " and suites[2] == suites[3] and suites[3] == suites[4]:\n", + " \n", + " return 1\n", + " \n", + " return 0" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "flush(hand_tups)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [], + "source": [ + "def full_house(hand_tups):\n", + " \n", + " numeric_vals = [tup[0] for tup in hand_tups]\n", + " \n", + " if three_of_a_kind(hand_tups) > 0:\n", + " triple = three_of_a_kind(hand_tups)\n", + " \n", + " while triple in numeric_vals:\n", + " numeric_vals.remove(triple)\n", + " \n", + " if numeric_vals[0] == numeric_vals[1]:\n", + " return 1\n", + " \n", + " return 0" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "full_house(hand_tups)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "def four_of_a_kind(hand_tups):\n", + " numeric_vals = [tup[0] for tup in hand_tups]\n", + " \n", + " for val in numeric_vals:\n", + " if numeric_vals.count(val) == 4:\n", + " return val\n", + " \n", + " return 0" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "def straight_flush(hand_tups):\n", + " if flush(hand_tups) > 0 and straight(hand_tups) > 0:\n", + " return flush(hand_tups)\n", + " else:\n", + " return 0" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "def royal_flush(hand_tups):\n", + " if straight_flush(hand_tups) == 10:\n", + " return 1\n", + " else:\n", + " return 0" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [], + "source": [ + "def rank_vals(hand_tups):\n", + " \"\"\"\n", + " return a list of values for\n", + " [royal_flush, straight_flush, four_of_a_kind, full_house,\n", + " flush, straight, three_of_a_kind, two_pairs, one_pair, \n", + " high_card]\n", + "\n", + " \"\"\"\n", + " ranks = []\n", + " \n", + " for rank in [royal_flush, straight_flush, four_of_a_kind, full_house,\n", + " flush, straight, three_of_a_kind, two_pairs, one_pair, \n", + " high_card]:\n", + " \n", + " ranks.append(rank(hand_tups))\n", + " \n", + " return ranks" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 0, 0, 1, 0, 0, 2, 1, 5, 5]" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "rank_vals(hand_tups)" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [], + "source": [ + "def compare(hand_tups_1, hand_tups_2):\n", + " \"\"\"\n", + " returns 1 if the first hand wins,\n", + " -1 if the second hand wins, \n", + " 0 if both are tied exactly\n", + " \n", + " \"\"\"\n", + " ranks_1 = rank_vals(hand_tups_1)\n", + " ranks_2 = rank_vals(hand_tups_2)\n", + " \n", + " for i in range(len(ranks_1)):\n", + " \n", + " if ranks_1[i] > ranks_2[i]:\n", + " return 1\n", + " elif ranks_1[i] < ranks_2[i]:\n", + " return -1\n", + " else: # if ranks_1[i] == ranks_2[i]:\n", + " continue\n", + " \n", + " # if all ranks are equal\n", + " return 0" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n", + "2\n" + ] + } + ], + "source": [ + "## tinkering\n", + "def return_tuple():\n", + " return 1, 2\n", + "\n", + "a, b = return_tuple()\n", + "\n", + "print(a)\n", + "print(b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Summary of functions\n", + "* card_tuple_from_str(card_str)\n", + " * outputs a tuple of a numeric value and a suite char\n", + "* read_hand_string(line)\n", + " * returns two lists of card tuples, for player 1 and 2\n", + " * \n", + "* Rank functions\n", + " * high_card(hand_tups)\n", + " * one_pair(hand_tups)\n", + " * ...\n", + " * royal_flush(hand_tups)\n", + "* rank_val(hand_tups)\n", + " * returns a list of rank vals from royal_flush to high_card\n", + "* compare(hand_tups_1, hand_tups_2)\n", + " * returns 1 if hand_tups_1 > hand_tups_2, \n", + " -1 if hand_tups_1 < hand_tups_2,\n", + " 0 if equal\n", + "* " + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "376\n" + ] + } + ], + "source": [ + "## solution code\n", + "player_1_win_count = 0\n", + "\n", + "with open('p054_poker.txt') as file:\n", + " \n", + " for line in file:\n", + " hand_tups_1, hand_tups_2 = read_hand_string(line)\n", + " \n", + "# print(hand_tups_1) # error catching\n", + " # found an error in card_tuple_from_str\n", + " \n", + " if compare(hand_tups_1, hand_tups_2) > 0:\n", + " player_1_win_count += 1\n", + " \n", + "print(player_1_win_count)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Final answer\n", + "Player 1 wins 376 games\n", + "\n", + "Time elapsed:\n", + "~6:30 - 7:42\n", + "\n", + "It took me a while just to work up the motivation to start coding. I envisioned that the code wouldn't be difficult, but perhaps just a bit tedious..." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/s055.ipynb b/s055.ipynb new file mode 100644 index 0000000..a33ea74 --- /dev/null +++ b/s055.ipynb @@ -0,0 +1,291 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Lychrel Numbers\n", + "https://projecteuler.net/problem=55" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem Statement\n", + "If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.\n", + "\n", + "Not all numbers produce palindromes so quickly. For example,\n", + "\n", + "349 + 943 = 1292,\n", + "\n", + "1292 + 2921 = 4213\n", + "\n", + "4213 + 3124 = 7337\n", + "\n", + "That is, 349 took three iterations to arrive at a palindrome.\n", + "\n", + "Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).\n", + "\n", + "Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.\n", + "\n", + "How many Lychrel numbers are there below ten-thousand?\n", + "\n", + "NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Planning\n", + "Write a function that chekcs if a number is a palindrome\n", + "\n", + "Write a function that sums a number with its reverse\n", + "\n", + "Write a function that returns true if a number achieves a palindrome under 50 iterations" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "def is_palindrome(x):\n", + " \"\"\"\n", + " x: string\n", + " \"\"\"\n", + " \n", + " if len(x) <= 1:\n", + " return True\n", + " \n", + " else:\n", + " if x[0] == x[-1]:\n", + " return is_palindrome(x[1:-1])\n", + " else:\n", + " return False\n", + " \n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "is_palindrome('bob')" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "is_palindrome('carl')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def reverse(x):\n", + " \"\"\"\n", + " x: int\n", + " \"\"\"\n", + " \n", + " x_str = str(x)\n", + " x_str_reverse = x_str[-1::-1]\n", + " \n", + " return int(x_str_reverse)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "54321" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "reverse(12345)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def reverse_and_sum(x):\n", + " \n", + " return x + reverse(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def is_lychrel(x):\n", + " \n", + " reverse_sum = reverse_and_sum(x)\n", + " counts = 1\n", + " \n", + " while not is_palindrome(str(reverse_sum)):\n", + " reverse_sum = reverse_and_sum(reverse_sum)\n", + " \n", + " if counts >= 50:\n", + " return True\n", + " \n", + " counts += 1\n", + " \n", + " return False\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "is_lychrel(4994)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## testing\n", + "is_lychrel(11)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "249\n" + ] + } + ], + "source": [ + "# solution\n", + "\n", + "# iterate over all values under 10,000\n", + "lychrel_count = 0\n", + "\n", + "for i in range(10000):\n", + " if is_lychrel(i):\n", + " lychrel_count +=1\n", + " \n", + "print(lychrel_count)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solution\n", + "There are 249 numbers under 10,000 whose reverse sum sequence does not reach a palindrome in under 50 iterations\n", + "\n", + "Time taken: ~8 to ~8:30" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}