Grid Puzzle

Given a square grid of size N, where the horizontal rows are numbered 1 to N from top to bottom and the vertical columns are numbered 1 to N from left to right. You must place a number in each cell of the N by N grid such that :-

• Each row is unique.
  
• Each row is exactly equal to one of the columns, however, it must not bethe column with the same index as the row.
  
• If X is the largest number you place in the grid, then you must also place1,2,...,X-1, where the condition X ≤ N is satisfied.
  

For a 4 × 4 grid, you may have the following matrix

defined by the following equalities:

• c1 = r4
• c2 = r3
• c3 = r2
• c4 = r1

This project outline was designed by the MET department at the German University in Cairo link.