Solution To: Home Sweet Home

Here was the original problem:

Arrange the numerals 1 through 8 in the figure so that no two consecutive integers touch at a side or on a corner.

Here is the solution:

Now, you might be thinking that your answer doesn't match this one.  I'd be willing to bet that it does (assuming your answer is correct), you just don't realize it.  There are 3 other solutions to this puzzle that are essentially the same as this one.  First you have the mirror image of this solution (specifically, in math terms, this solution is a reflection of the original solution over the y-axis):

Then you have another mirror image of the original solution (specifically, a reflection of the original solution over the x-axis):

The last solution is a 180 degree rotation of the original solution (or a double reflection, once over the x-axis and then once over the y-axis, or vice versa).

In math, we would consider all four of these solutions to be the same solution, because although they look different, they aren't unique solutions.  That was probably way more information than you wanted. :)

See you back here next week for more fun!

Sincerely,
The Math Freak