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Thursday, September 15, 2011

Answer for Challenging Question#3

First figure out what the total is.  If each row adds up to t, then all three rows add up to 3t.  Yet this is all the numbers 1 through 9, hence 3t = 1+2+3+4+5+6+7+8+9 = 45, and t is 15.
Next consider the for lines passing through the middle square.  Taken together, these numbers add up to 4×15 = 60.  Yet this is just the numbers 1 through 9, where the middle entry is used another 3 times over.  Thus 3 times the middle is 60 - 45, and the middle square is 5.  Some trial and error reveals the pattern.
2 9 4
7 5 3
6 1 8


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