Problem 389
Platonic Dice

An unbiased single 4-sided die is thrown and its value, T, is noted.
T unbiased 6-sided dice are thrown and their scores are added together. The sum, C, is noted.
C unbiased 8-sided dice are thrown and their scores are added together. The sum, O, is noted.
O unbiased 12-sided dice are thrown and their scores are added together. The sum, D, is noted.
D unbiased 20-sided dice are thrown and their scores are added together. The sum, I, is noted.
Find the variance of I, and give your answer rounded to 4 decimal places.

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http://projecteuler.net/problem=389