From ed pegg Is there a list of smallest multiplicative constants for various NxN squares somewhere?
Back to the original question asked by Ed, here is the answer! You will find below the 10 smallest multiplicative constants for 3x3 and for 4x4 MAGIC squares. Ed, I can provide you a longer list if you want. For SEMI-MAGIC squares (not taking care of the diagonals), the smallest magic product is 120 for 3x3 with for example 1 20 6 12 2 5 10 3 4 with 3 magic rows, 3 magic columns (and 1 magic diagonal!!... but it was not asked for semi-magic squares), and is 4320 for semi-magic 4x4 as we have seen last week. Best regards. Christian. ---- 3x3 multiplicative squares Prod. = 2^ * 3^ * 5^ * 7^ * 11^ 216 3 3 0 0 0 1000 3 0 3 0 0 1728 6 3 0 0 0 2744 3 0 0 3 0 3375 0 3 3 0 0 4096 12 0 0 0 0 5832 3 6 0 0 0 8000 6 0 3 0 0 9261 0 3 0 3 0 10648 3 0 0 0 3 ---- 4x4 multiplicative squares Prod. = 2^ * 3^ * 5^ * 7^ * 11^ 5040 4 2 1 1 0 6480 4 4 1 0 0 6720 6 1 1 1 0 7200 5 2 2 0 0 7560 3 3 1 1 0 7920 4 2 1 0 1 8400 4 1 2 1 0 8640 6 3 1 0 0 9072 4 4 0 1 0 9240 3 1 1 1 1 ----