⍝ N-Queens — count solutions to placing N non-attacking queens on N×N
⍝
⍝ A solution is encoded as a permutation P of 1..N where P[i] is the
⍝ column of the queen in row i.  Rows and columns are then automatically
⍝ unique (it's a permutation).  We must additionally rule out queens
⍝ sharing a diagonal: |i-j| = |P[i]-P[j]| for any pair.
⍝
⍝ Backtracking via reduce — the classic Roger Hui style:
⍝   queens ← {≢{⍵,¨⍨↓(0=∊(¨⍳⍴⍵)≠.+|⍵)/⍳⍴⍵}/(⍳⍵)⍴⊂⍳⍵}
⍝
⍝ Plain reading:
⍝   permute 1..N, keep those where no two queens share a diagonal.
⍝
⍝ Known solution counts (OEIS A000170):
⍝     N    1   2   3   4   5   6   7    8    9    10
⍝   q(N)   1   0   0   2  10   4  40   92  352   724

queens ← {≢({(i j)←⍺⍵ ⋄ (|i-j)≠|(P[i])-(P[j])}⌿permutations ⍵)}