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Wednesday, July 30, 2008

Nineteen Numbers Net

This is the toughest number net on our site! It has nineteen circles that have to be filled with the numbers 1 up to (and including) 19. These numbers have to be placed in such a way that all numbers on any horizontal row and any diagonal line add up to the same sum.

Warning: There are many horizontal and diagonal lines, which have a different number of circles (3, 4, or 5), nevertheless all these sums have to be equal!

The Question: How should the nineteen numbers be placed in the net?

Answer: As you probably found out, finding the right position for all nineteen numbers in the net is certainly not an easy task. There are 12 possible solutions, but in fact they are all rotation and mirror symmetrical variants of one and the same solution. This solution has a sum of 38 on any of its horizontal and diagonal rows, and is shown below:

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