55 lines
1.7 KiB
Markdown
55 lines
1.7 KiB
Markdown
---
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id: 5900f4e51000cf542c50fff7
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title: 'Problem 376: Nontransitive sets of dice'
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challengeType: 5
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forumTopicId: 302038
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dashedName: problem-376-nontransitive-sets-of-dice
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---
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# --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 Die B: 2 2 2 5 5 5 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 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 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 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. 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. Dice with the same set of pips are equal, regardless of which side on the die the pips are located. The same pip value may appear on multiple dice; if both players roll the same value neither player wins. 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. How many are there for N = 30 ?
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# --hints--
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`euler376()` should return 973059630185670.
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```js
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assert.strictEqual(euler376(), 973059630185670);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler376() {
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return true;
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}
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euler376();
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```
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# --solutions--
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```js
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// solution required
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```
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