Technique for solving numerical cryptograms?

[DyslexicHobo]

I'm sure everyone here has seen one of these things some time or another. Where you're given something like...

SEND
+MORE
______
MONEY

...and then you have to figure out what each letter represents as a number in order to make the solution make sense, and no two letters can equal the same number, and no number in front can equal zero.


This particular gram that I posted I already know the answer for, but is there a specific way to solve these?

I was thinking about using a systems of equations somehow, maybe...

1000s + 100e + 10n + d + 1000m + 100o + 10r + e = 10000m + 1000o + 100n + 10e + y.

... however I'm not sure how I'd get enough other equations to substitute!

There's got to be an easy, mathematical way to do these. Anyone got some ideas?

 

[fresh_42]

Mathematically you get an underdetermined system of equations which cannot be solved.
Computationally this is an example for a TM with oracle band, i.e. guessed numbers can be verified quickly.

Considering nowadays possibilities, an algorithm which checks solutions would be the method of choice.