Ah, I see.
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If we perform the operation on parities, we can see that all numbers turn even after at most 4 steps.
If we consider symmetry/rotation, these two sequences cover all possible cases.
EOEE
OOEE
EOEO
OOOO
EEEE
EOOO
OEEO
OEOE
OOOO
EEEE
How to continue from here?
Well, once all numbers are even, we consider the parity of all numbers divided by two.
By the same argument, we'll only get numbers divisible by 4 after the next round. Then only numbers divisible by 8. Since all numbers are <=100, we must eventually end up with 0 0 0 0, since these are the only numbers that are divisible by any number.