## On the Subject of The Shaker

Let's shake things up, shall we?

This module will contain sixteen balls, each labeled with a unique number from zero to nineteen (inclusive). You must input four numbers into the module to solve it.

To input a number, set the four lights to their proper statuses and press the center of the module. The number when all of the lights are off is zero. The bottom-right light represents adding one to the number, the bottom-left two, the top-right four, and the top-left eight.

To determine the numbers to input, take the following steps:

• Take the four numbers missing from the balls (call them a–d in order from greatest to smallest)

• Add 10 to each and multiply them together

• Associate the 4 least significant digits of this product with a–d

• Order by the associated digits (then by the original number in case of ties)

• Convert a–d to new numbers according to the below table and submit those in the new order

Ordered Number | Submitted Number | Ordered Number | Submitted Number |
---|---|---|---|

0 | 15 | 10 | 9 |

1 | 6 | 11 | 7 |

2 | 14 | 12 | 3 |

3 | 0 | 13 | 11 |

4 | 7 | 14 | 9 |

5 | 15 | 15 | 4 |

6 | 1 | 16 | 12 |

7 | 8 | 17 | 3 |

8 | 5 | 18 | 5 |

9 | 2 | 19 | 13 |