18 7 9 16 20 5 11 25 24 1 8 17 19 6 10 15 21 4 12 13 23 2 14 22 3

Wow! Did you compute that or look it up in the internet?

I would have named it a "Magic" 'Row'." "Rectangle" implies there is something two-dimensional about and required of it. Otherwise, the solution given is surprising to me. How many total solutions are there, counting all reflections/rotations?

The steps for getting that solution are: The possible squares from a sum of two numbers from 1 to 25 are: 4,9,16,25,36,49 You must start with 18, the number with only one possible neighbour. And notice that some numbers have only two neighbours: 16 (9,20), 17 (8,19), 19 (6,17), 20 (5,16), 21 (4,15), 22 (3,14), 23 (2,13) Then some combinations are must be in this order or the reverse one (9,16,20,5), (8,17,19,6)

Arrange your tan wrote: I would have named it a "Magic" 'Row'." "Rectangle" implies there is something two-dimensional about and required of it. Well, you have to fill in the "boxes" of the rectangle, so a certain sum is achieved (similar to the magic squares concept).

No, you don't have to fill in the "boxes" of the/a rectangle, because a row with its entries STILL satisfies a certain sum being achieved, hence the "Magic" Row.

It does, but in this specific problem, they ask you to write the numbers down in a rectangle. >.>

Here is another solution: (which I worked out using the steps mc said - with the neighbors of numbers) 18 7 9 16 20 5 11 25 24 12 4 21 15 10 6 19 17 8 1 3 22 14 2 23 13 This happens to be the first solution with two sections reversed....pretty cool,...i was working to get the first solution but got this instead....