*Originally posted by forkedknight*

**How about peoples' methods for solving this one and/or other similar puzzles in general.
**

I created an Excel spreadsheet and played around with relationship formulas and error conditions. I can email it to you if you'd like to see it.

We coded a general solver for this type of problem in SCHEME/LISP in my artificial intelligence class at university last semeseter. I didn't have that code handy for this problem though.

Well, the method which worked for me is as follows.

In initially working with the problem, I noticed two additions..

A + D = N

A + F = N

Based on this, one of the two have a carry added in, the other does not.

In addition to this, A cannot be 0 or 9, or else A = N.

N can't be 0 as it starts a number, and for some reason, I had eliminated N = 9 as well. The reason may come to me.

At any rate, since the two sums occur beside each other, I can determine what D and F are from A and N.

I simply tried each combination of A and N, eliminating first those where I had matching numbers, as well as those where A + N + 1 resulted in no carry (since R + 0 = T...)

Each test was straightforward, with solving for E leading to quick judgment of each case.