**The 8-Queens Problem :**The Bounding function for 8-queens problem is

No two queens placed on the same column → x

_{i}'s are distinct

No two queens placed on the same diagonal → how to test?

The same value of "row-column" or "row+column" indicates that two queens placed on the same diagonal.

Supposing two queens on (i,j) and (k,1)

i-j=k-1(i.e,j-1=i-k) or i+j = k+1(i.e, j-1 = k-i)

So, two queens placed on the same diagonal iff

[j-i] = [i-k]