IBM Ponder This #174 · October 2012

There are seven polyhedral dice in a Dungeons & Dragons game. The result of throwing the 7 D&D dice is the sum of the seven numbers from each die:

1. Tetrahedron: numbers 1, 2, 3, 4
2. Cube: numbers 1, 2, 3, 4, 5, 6
3. Octahedron: numbers 1, 2, 3, 4, 5, 6, 7, 8
   4, 5. Two pentagonal trapezohedron: numbers 0,1, 2, 3, 4, 5, 6, 7, 8, 9
4. Dodecahedron: numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
5. Icosahedron: numbers 1, 2, 3, ..., 20.

Find a way to get the same distribution (same probability for each result) of tossing all seven D&D cubes by tossing four Disdyakis Triacontahedrons with integer numbers between 1 and 17 on their 120 faces.

Please supply your answer as four lines of 17 numbers. Line i describes the i-th Disdyakis Triacontahedron and Column j describes how many times the number j appears on it.

Solution

Best opened after a real attempt

To be added.