From a71f6c77a86c72fb2616689978e527e093b3b9ad Mon Sep 17 00:00:00 2001 From: Mike Nsubuga Date: Fri, 29 Jul 2022 19:14:02 +0300 Subject: [PATCH 1/3] updated explanation --- src/assets/card-content/en/cards/7D.json | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/assets/card-content/en/cards/7D.json b/src/assets/card-content/en/cards/7D.json index 5cb805e..37b3ae3 100644 --- a/src/assets/card-content/en/cards/7D.json +++ b/src/assets/card-content/en/cards/7D.json @@ -7,7 +7,7 @@ "statement": "

What is the biggest number of pieces of a circular cake you can obtain with 5 straight cuts? Cuts must be made on the top of the cake.

", "correct_answer": "16", "hint": "

Start with a small number of cuts, e.g. 1, 2, 3. How can you add another cut to get the biggest number of pieces? Remember it doesn't say that the pieces have to be of the same size! What happens if many cuts pass through the same point?

", - "explanation": "

It is best to start with a simpler question and look for patterns. Start by looking at a square. There are two different ways we could slice the cake.

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For a pentagon there are five ways:

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For a hexagon there are 14 ways as you can see below:

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In this diagram you can see the solution is found by thinking of 6 + 3 + 2 + 3 = 14, but you can arrive at the solution by using the solutions for smaller polygons: If we consider the side of the hexagon connecting points 1 and 2, it can form a triangle with any of the other 4 points. If we pick point 3 or 6, we are left with a pentagon, for which we know there are 5 ways of triangulating it. If we pick point 4 or 5, we are left with a triangle and a square, for which there are 1\u00d72 ways. Adding up the number of choices gives us 5 + 2 + 2 + 5 = 14. The equivalent combination for the pentagon is 2 + 1 + 2 = 5, where 1 is the result of the triangle (which has of course only one option) and 2 is the result for a square.

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This is a more useful technique for moving on to thinking of polygons with more vertices.

" + "explanation": "

With one cut you always get 2 pieces. With two cuts you can get 4 pieces. With three cuts, if all cuts pass through the same point you get 6 pieces. However, you can get 7 pieces if the third cut doesn’t pass through the same point as the previous two. Use this idea to get the maximum number with four cuts. So to get the most pieces, make sure that no more than two cuts pass through the same point, otherwise you get less pieces. With four cuts you can get 11 pieces. Do the same again for five cuts, start with the four cuts that give 7 pieces and add a cut without passing through any meeting points (intersections) and you can get 16 pieces.

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\"\"" }, "extension_1": { "statement": "

What is the biggest number of pieces of cake you can obtain with 7 cuts?

", From 6665b6e28a59aa6360a86160119ae5e9cf527033 Mon Sep 17 00:00:00 2001 From: Mike Nsubuga Date: Fri, 29 Jul 2022 19:16:17 +0300 Subject: [PATCH 2/3] updated css for 7D image --- src/app/components/cards.component.scss | 3 +++ 1 file changed, 3 insertions(+) diff --git a/src/app/components/cards.component.scss b/src/app/components/cards.component.scss index 55ac097..1b42a44 100644 --- a/src/app/components/cards.component.scss +++ b/src/app/components/cards.component.scss @@ -274,6 +274,9 @@ div p { .Table_Handshakes_image_0{ width: 50%; } +.Pieces_of_Cake_image_0.png{ + width: 50%; +} .Table_Handshakes_image_1{ width: 50%; } From fe9bca2cba3aef9f2f9ca7c95a17e9052ae1878d Mon Sep 17 00:00:00 2001 From: Mike Nsubuga Date: Fri, 29 Jul 2022 19:16:53 +0300 Subject: [PATCH 3/3] update css 7D --- src/app/components/cards.component.scss | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/app/components/cards.component.scss b/src/app/components/cards.component.scss index 1b42a44..02e2dc4 100644 --- a/src/app/components/cards.component.scss +++ b/src/app/components/cards.component.scss @@ -274,7 +274,7 @@ div p { .Table_Handshakes_image_0{ width: 50%; } -.Pieces_of_Cake_image_0.png{ +.Pieces_of_Cake_image_0{ width: 50%; } .Table_Handshakes_image_1{