yaworsw/euler-manager

---
:id: 376
:name: Nontransitive sets of dice
:url: https://projecteuler.net/problem=376
:content: "Consider the following set of dice with nonstandard pips:\n\nDie A: 1 4
  4 4 4 4  \nDie B: 2 2 2 5 5 5  \nDie C: 3 3 3 3 3 6\n\nA game is played by two players
  picking a die in turn and rolling it. The player who rolls the highest value wins.\n\nIf
  the first player picks die A and the second player picks die B we get  \nP(second
  player wins) = <sup>7</sup>/<sub>12</sub> \\> <sup>1</sup>/<sub>2</sub>\n\nIf the
  first player picks die B and the second player picks die C we get  \nP(second player
  wins) = <sup>7</sup>/<sub>12</sub> \\> <sup>1</sup>/<sub>2</sub>\n\nIf the first
  player picks die C and the second player picks die A we get  \nP(second player wins)
  = <sup>25</sup>/<sub>36</sub> \\> <sup>1</sup>/<sub>2</sub>\n\nSo whatever die the
  first player picks, the second player can pick another die and have a larger than
  50% chance of winning.  \nA set of dice having this property is called a **nontransitive
  set of dice**.\n\nWe wish to investigate how many sets of nontransitive dice exist.
  We will assume the following conditions:\n\n- There are three six-sided dice with
  each side having between 1 and <var>N</var> pips, inclusive.\n- Dice with the same
  set of pips are equal, regardless of which side on the die the pips are located.\n-
  The same pip value may appear on multiple dice; if both players roll the same value
  neither player wins.\n- The sets of dice {A,B,C}, {B,C,A} and {C,A,B} are the same
  set.\n\nFor <var>N</var> = 7 we find there are 9780 such sets.  \nHow many are there
  for <var>N</var> = 30 ?\n\n"