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tkoz0 committed Dec 17, 2024
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Expand Up @@ -733,6 +733,159 @@ <h3 id="dec15">Dec 15</h3>

<h3 id="dec16">Dec 16</h3>

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<g fill="black" font-size="0.05em">
<text x="0.5" y="10">How many ways can</text>
<text x="0.5" y="11">you tile the shape with</text>
<text x="0.5" y="12">2 &times; 1 dominoes?</text>
</g>
</svg>

<p>
First consider a domino along the thin edge. There are 2 possibilities shown
below.
</p>

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</svg>

<p>
In the first possibility, placing a domino adjacent on the left of the red tile
leaves a single space that cannot be filled with a \(2&times;1\) domino. So we
use the second possibility. By applying similar reasoning to the other 4 edges,
we must have dominoes in the following positions.
</p>

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<rect x="1" y="5" width="1" height="2" />
</g>
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</g>
</svg>

<p>
This leaves 4 \(2&times;2\) spaces. Each of these has 2 possibilities: 2
vertical dominoes or 2 horizontal dominoes. The total number of possible tilings
is \(2^4=16\).
</p>

<h3 id="dec17">Dec 17</h3>

<h3 id="dec18">Dec 18</h3>
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