[Solved]Change the elements of a matrix so it becomes a matrix with just 0s

Question

Hi SoloLearn. I need some help with this problem: I have a binary matrix, let's say this one:
0 1 1 0
0 1 0 1
0 0 1 1
0 0 0 0
0 0 0 0
Every element has a "switch" that changes the element from 1 to 0 or viceversa, but it also changes the 2X2 square with that element as the right-bottom element. So the switch (i,j) changes: (i,j)(i-1,j)(i-1,j-1)(i,j-1).
I can or cannot find a sequence that will turn all the elements in 0s.
I have to say if there is or not any solution to this puzzle.
Thanx! :)

Answer 1

Assuming i is 0->4, top to bottom
and j is 0->3, left to right

0110
0101
0011
0000
0000

switch (1, 2)

0[1][1]0
0[1]{0}1
0011
0000
0000

0000
0011
0011
0000
0000

switch (2, 3)

0000
00[1][1]
00[1]{1}
0000
0000

0000
0000
0000
0000
0000

There are multiple solutions

Answer 2

jtrh Yes, there may be multiple solutions, but I must write a program that solves or not a random puzzle.

Answer 3

*** That is allowed, but it will only change the lights that are in the matrix.

Answer 4

I found a solution that I think uses Greedy, but I don't know if that will always work or not. I search for elements of 1 and when I find one, let's say (I,j), I switch (I+1,j+1)

Answer 5

*** Thank you for your help, I think this solutions works. Have a great day:)