Cryptarithmetic

Cryptarithmetic example: https://developers.google.com/optimization/puzzles/cryptarithmetic

      CP
+     IS
+    FUN
--------
=   TRUE

The challenge is to find integers to swap out for each letter such that the equation holds true. This is a constrained programming problem, and can be re-cast in terms of an arbitrary radix as follows:

The "tens" place becomes the expression $ \mbox{(C+I+F)}\times(\mbox{base}) $ on the left side and $ \mbox{T}\times(\mbox{base}) $ on the right.

The "ones" place becomes the expression $ \mbox{P+S+N} $ on the left and $ \mbox{E} $ on the right, which, combining, gives:

$ \mbox{(C+I+F)}\times(\mbox{base}) + \mbox{P+S+N} = \mbox{T}\times(\mbox{base}) + \mbox{E} $