---
id: 5900f4e51000cf542c50fff7
challengeType: 5
title: 'Problem 376: Nontransitive sets of dice'
---

## Description
<section id='description'>
Consider the following set of dice with nonstandard pips:



Die A: 1 4 4 4 4 4
Die B: 2 2 2 5 5 5
Die C: 3 3 3 3 3 6


A game is played by two players picking a die in turn and rolling it. The player who rolls the highest value wins.



If the first player picks die A and the second player picks die B we get
P(second player wins) = 7/12 > 1/2


If the first player picks die B and the second player picks die C we get
P(second player wins) = 7/12 > 1/2


If the first player picks die C and the second player picks die A we get
P(second player wins) = 25/36 > 1/2


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.



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.

For N = 7 we find there are 9780 such sets.
How many are there for N = 30 ?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler376()</code> should return 973059630185670.
    testString: assert.strictEqual(euler376(), 973059630185670, '<code>euler376()</code> should return 973059630185670.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler376() {
  // Good luck!
  return true;
}

euler376();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>
