can anyone proove it. ie, using algebra, i have been thinking about it but i always find it easier when i know the answer
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Total=0=(0/2)²
1 4 3
3 2 1
Total = 2²
1 3 2
4 2 2
Total = 2²
2 4 2
3 1 2
Total = 2²
2 3 1
4 1 3
Total = 2²
3 2 1
4 1 3
Total = 2²
Is that all of them?
]]>Total=1=(2/2)²
]]>It seems logical. Let's try a 6 row one (1 to 12):
1 12 11
3 10 7
4 8 4
5 7 2
9 6 3
11 2 9
Total = 36
That is 6²
]]>That's 100!
Re-arranging,
1 17 16
2 20 18
3 13 10
4 19 15
5 16 11
6 18 12
7 15 8
8 14 6
9 11 2
10 12 2
100 yet again!
Should it be always (n/2)² for 0 to n???
(Just like the side total of a magic square containing numbers 1 to n² is
(n³+n)/2 ??? )
25
]]>In the examples above, color or shade (in the first two columns) the numbers 1, 2, 3, 4, and 5. Do you see a pattern?
]]>I think NIH might have had a typo when telling us the second one...
Thanks -- it's fixed now!
Of course, this comes from the well known result, first proved by Euler, that pi^2/6 = 1/1^2 + 1/2^2 + 1/3^2 + ...
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