92 lines
2.0 KiB
Markdown
92 lines
2.0 KiB
Markdown
---
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id: 5900f4e51000cf542c50fff7
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challengeType: 5
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title: 'Problem 376: Nontransitive sets of dice'
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---
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## Description
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<section id='description'>
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Consider the following set of dice with nonstandard pips:
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Die A: 1 4 4 4 4 4
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Die B: 2 2 2 5 5 5
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Die C: 3 3 3 3 3 6
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A game is played by two players picking a die in turn and rolling it. The player who rolls the highest value wins.
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If the first player picks die A and the second player picks die B we get
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P(second player wins) = 7/12 > 1/2
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If the first player picks die B and the second player picks die C we get
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P(second player wins) = 7/12 > 1/2
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If the first player picks die C and the second player picks die A we get
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P(second player wins) = 25/36 > 1/2
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So whatever die the first player picks, the second player can pick another die and have a larger than 50% chance of winning.
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A set of dice having this property is called a nontransitive set of dice.
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We wish to investigate how many sets of nontransitive dice exist. We will assume the following conditions:There are three six-sided dice with each side having between 1 and N pips, inclusive.
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Dice with the same set of pips are equal, regardless of which side on the die the pips are located.
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The same pip value may appear on multiple dice; if both players roll the same value neither player wins.
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The sets of dice {A,B,C}, {B,C,A} and {C,A,B} are the same set.
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For N = 7 we find there are 9780 such sets.
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How many are there for N = 30 ?
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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>euler376()</code> should return 973059630185670.
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testString: assert.strictEqual(euler376(), 973059630185670, '<code>euler376()</code> should return 973059630185670.');
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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 euler376() {
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// Good luck!
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return true;
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}
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euler376();
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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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