There are 25 primes smaller than 100. What is the closest to a 5 x 5 magic square I can construct with them? By "closest" I mean the one with the most columns, rows, and diagonals (12 in all) adding to the same amount.
$\begingroup$
$\endgroup$
asked Sep 4, 2022 at 14:15
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
4
I'll get things started with
10 lines with common sum 215:
23 47 31 43 71
89 41 67 11 7
13 29 17 97 59
53 79 2 61 5
37 19 83 3 73
You can achieve
12 lines with distinct primes, here with common sum 283:
13 107 79 37 47 97 19 7 71 89 29 17 131 23 83 113 3 5 109 53 31 137 61 43 11
-
7$\begingroup$ This is clearly optimal: the row/column containing 2 will have an even sum, all others will have an odd sum. $\endgroup$ Sep 4, 2022 at 17:52
-
1$\begingroup$ Followup: By choosing any 25 primes (not necessarily the 25 smallest), can you achieve 11 or even 12 matching sums? $\endgroup$ Sep 5, 2022 at 7:02
-
1$\begingroup$ @EdMurphy I updated my answer to address this. $\endgroup$– RobPrattSep 5, 2022 at 16:16
-