## Platonic Dice

### Problem 389

Published on 16 June 2012 at 05:00 pm [Server Time]

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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