08 Apr '06 00:41>
Originally posted by CrazyLilTingCommon sense is in fact the answer. Say you have your square a,b,c,d you know set the values to the zeros or same numbers required. Then you find the next square and see what it contains, as you are working in general cases you have a proof.
with all due respect:
can you probe that they are true and why?
I don't want to waste the rest of my life checking them using "general examples".
Sincerely, I will appreciate it. May be induction is the key word.
Honestly, I don't know.
I must to confess that my skill at math problems is way too poor.
Regards
- Julia
ps: I'm sure that common sense isn't the answer
So say we are looking at two adjacent zeros. We have 0,b,c,0 (from top left clockwise, so the zeros are the two left numbers). Finding the next square we find 0,b,abs(b-c),c . So if b and c are different we have a new square with one zero (which is a different case) and if they are the same we have a new square with non-adjacent zeros (as abs(b-c) would now be zero also).
That's all there is to it.