Cryptarithmetic example:

      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 "thousands" place has nothing on the left side, and a ${\displaystyle {\mbox{T}}}$ on the right side.

The "hundreds" place has an ${\displaystyle F}$ on the left side and a ${\displaystyle {\mbox{R}}}$ on the right side.

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

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

${\displaystyle Fr^{2}+(C+I+U)r+(P+S+N)=Tr^{3}+Rr^{2}+Ur+E}$

We can also limit the search space by constraining C, I, F, T to be nonzero.

We have 10 letters total, CPISFUNTRE, and of those 6 that are possibly (0 through base) and 4 which are possibly (1 through base), for a total search space of

${\displaystyle b^{6}(b-1)^{4}}$

${\displaystyle 10^{6}\times 9^{4}=6,561,000,000=6.56\times 10^{9}}$