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