# 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.

**柏拉图多面体骰子**

掷一个无偏的正四面体骰子，记点数为T。

掷T个无偏的正六面体骰子，记点数和为C。

掷C个无偏的正八面体骰子，记点数和为O。

掷O个无偏的正十二面体骰子，记点数和为D。

掷D个无偏的正二十面体骰子，记点数和为I。

求I的方差，并将你的答案四舍五入到4位小数。