KöMaL 2012 K352

Make a 5×5 table, and fill it out with the numbers 1 to 25, left to right, top to bottom. Interchange the rows an arbitrary number of times, and then interchange the columns an arbitrary number of times. Add 7 to each entry of the ``mixed'' table obtained in this way. Finally, add the numbers along one of the diagonals. Prove that the result is always 100. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25