This one may take a bit of time. It is a version of the classic "put numbers in the boxes such that all rows, and diagonals add up to the same number.
Here is an interesting version:
The attached image 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.
Be careful: there are many horizontal and diagonal lines, and 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?
There are at least 12 solutions, but as far as I know, all of them are simply mirror images or rotations. Perhaps the best way to answer this one is to tell us what the sum for this puzzle is.
Any idea for a solution method, short of brute force? Some of the conclusions I drew based on my analysis were accurate, while others were only close, so my approach was clearly not the best. I'm glad you posted the answer before I tired all 19! possibilities
Sorry, but in this case, it is a problem I found and did not actually do the solution myself. I usually try them myself, but I was running short of time, so I took one that I had already with the answer.
