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Bill Markwick, 02/07/45 - 24/06/24
I'm sorry to have to tell you that Dad passed away in June. He had several health problems but his love of maths and puzzles never faded, as you can see from this site. One of the last things he did before he left us was to post the Magic Polygons items below.
I'll leave this site up in his memory.
Andrew Markwick, July 2024.
2024 W/e 21/6/24
Click on link below for 3x3 Magic Square Multiplication M17
MS 17 3x3 Magic Square Multiplied
You have been told that the digits 1-9 will not work.
Looking at the problem we need 9 numbers and 8 products, (3 rows, 3 columns and 2 diagonals), to find a common product.
When I wrote this question there are 2 known finite answers, both given in the answers, for the only other solutions need a computer.
One answer is:
18 1 12
4 6 9
3 36 2 Product 216
Factors of 216 are 1, 2, 3, 4, 5, 9, `8, 36, 72, 108, 216.
216 = 2^3.3^3
The second solution is:
128 1 32
4 16 64
8 256 2 Product 4096
Factor of 4096 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048 and 4096.
4096 = 2^12