82 lines
2.1 KiB
Markdown
82 lines
2.1 KiB
Markdown
---
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id: 5900f46c1000cf542c50ff7e
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challengeType: 5
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title: 'Problem 256: Tatami-Free Rooms'
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---
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## Description
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<section id='description'>
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Tatami are rectangular mats, used to completely cover the floor of a room, without overlap.
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Assuming that the only type of available tatami has dimensions 1×2, there are obviously some limitations for the shape and size of the rooms that can be covered.
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For this problem, we consider only rectangular rooms with integer dimensions a, b and even size s = a·b.
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We use the term 'size' to denote the floor surface area of the room, and — without loss of generality — we add the condition a ≤ b.
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There is one rule to follow when laying out tatami: there must be no points where corners of four different mats meet.
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For example, consider the two arrangements below for a 4×4 room:
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The arrangement on the left is acceptable, whereas the one on the right is not: a red "X" in the middle, marks the point where four tatami meet.
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Because of this rule, certain even-sized rooms cannot be covered with tatami: we call them tatami-free rooms.
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Further, we define T(s) as the number of tatami-free rooms of size s.
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The smallest tatami-free room has size s = 70 and dimensions 7×10.
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All the other rooms of size s = 70 can be covered with tatami; they are: 1×70, 2×35 and 5×14.
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Hence, T(70) = 1.
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Similarly, we can verify that T(1320) = 5 because there are exactly 5 tatami-free rooms of size s = 1320:
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20×66, 22×60, 24×55, 30×44 and 33×40.
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In fact, s = 1320 is the smallest room-size s for which T(s) = 5.
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Find the smallest room-size s for which T(s) = 200.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler256()</code> should return 85765680.
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testString: assert.strictEqual(euler256(), 85765680, '<code>euler256()</code> should return 85765680.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler256() {
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// Good luck!
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return true;
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}
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euler256();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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