numbers

[Dave Davison]

Rearrange numbers so they add up to the same number (less than 20) every way including diagonally. The quest is not simply how but how long it takes to solve. Cheers Dave

[HansV]

See Magic square

[AlanMiller]

Rearrange numbers so they add up to the same number (less than 20) every way including diagonally. The quest is not simply how but how long it takes to solve. Cheers Dave

About 5 seconds... done it once or twice before.
I've seen several ways to do this, but the one I reckon is easiest to remember is to form a "magic diamond" then just rotate it 45° to a square. You just transpose the corners over the top of the 5, onto the opposite grid intersection. So 1 ends up in the centre of the 5689 grid, 3 in the 4578 grid, 7 into the 2356 grid and 9 into the 1245 grid centre. The result is a diamond shape which can be rotated to a square.

Alan

[Graeme]

I first saw this at school. My solution is the same as in Hans' link except a mirror image. The rules were, start with 1 in the centre square in the top row. Always move up one row and across one column to the right. If the move takes you out of the grid move to the far end of the row or column you are now in. If there is already a number in the square then drop to the square below. From the top right corner, also drop to the square below. It's easier to see with a 5 square grid and works for any odd number of squares:

[AlanMiller]

Here's a better way of showing my method.

Write the numbers 1 to 9 in a 3x3 "open" grid (black & blue numbers).
Transpose the corner numbers over the top of the central 5, to the positions shown (black -> red).
This gives the grey diamond which then rotates to a magic square.

Alan

[HansV]

Nice!