---
id: 5900f4f21000cf542c510004
title: 'Problem 389: Platonic Dice'
challengeType: 5
forumTopicId: 302053
dashedName: problem-389-platonic-dice
---

# --description--

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.

# --hints--

`platonicDice()` should return `2406376.3623`.

```js
assert.strictEqual(platonicDice(), 2406376.3623);
```

# --seed--

## --seed-contents--

```js
function platonicDice() {

  return true;
}

platonicDice();
```

# --solutions--

```js
// solution required
```