Try to restore an interesting "magic square of squares", over two centuries old:
1. 16 distinct integers.
2. 4*4 matrix.
3. Each number is a square number.
4. No number is over 80^2 i.e. 6400.
5. Each row, column, and long diagonal sums up to 8515.
I'm not going to reproduce here the solution to this puzzle, but just giving a square close to the solution.
For easiness all the numbers of the 4x4 matrix below are replacing their squares (i. e.: 65 means 65^2, 53 means 53^2, and so on)
65 53 16 35
31 4 47 73
25 19 77 40
52 73 11 19
This is not compliant with the puzzle because the diagonals do not sum 8515.
But:
1) all the numbers are squares,
2) there are 16 distinct integers (see below)
3) no number is over 80 (i. e: 6400)
4) the rows and the columns sums up to 8515
5) the sum of both diagonals is two times 8515
PD: I'm aware that numbers 73 and 19 are repeated, but this can easily be solved writing: 73, (73), 19, (19). The puzzle just requires "16 distinct integers", not "positive integers".
Edited on January 7, 2018, 10:29 am

Posted by armando
on 20180107 09:51:09 