Challenge May-2023

Grid of Bulbs                                                                                            Solutions

“Next best action” is a popular decision-making strategy. But how to define the “best” next action? This challenge may demonstrate it. Consider an NxN grid of lightbulbs. We are given an initial state where some of the bulbs are off and some are on. Then, at every step you need to choose a bulb in the off state. It will turned on, and every other bulb in the row and in the column of the bulb will be toggled: If it was on, it turns off, and vice versa. The goal is to reach a grid where all the light bulbs are on. This problem was proposed by IBM.

Here is an example of an initial grid state with all next actions that lead to the final state:

Please submit your solutions using your favorite decision modeling tool.

Solutions: 

P.S. We assume that submitted solutions will be able to handle much larger grids like this one:

000001000000000001110011
110100010110101000010011
011101110000001101001110
000110111000110101101100
101101011010010011101010
111000100101110100101000
110001011100000000000101
100000010001100000000010
000110010010110110101001
011101101011111011100000
011000101010111011111100
100011110010000100100111
000111010010100010001110
011001010001001111110101
110001000010111000100000
000000101100101000101001
111001010010010011110110
100000110001111111011010
110100000011100100110010
101000110111001110010000
110000000010011100100101
111111011011111100010101
000000000110101011100000
110001111100000011001111