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