Can You Solve the Cryptogram?

Riddler Express

Reader Betts Slingluff enjoys holiday cryptarithms with the family and suggested that now was a good time for such a puzzle on The Riddler. This week’s Express is a spin on a cryptarithm originally by Frank Mrazik:

As with any cryptarithm, each letter represents one of the digits from 0 to 9, and different letters represent different digits.

The catch? This puzzle has two possible solutions — that is, two distinct sets of letter-to-number assignments. Can you find both solutions?

Solution

In the hundred thousands position, $L$ sums to $H$, which means $H = L + 1$.

This means in the ten thousands position, $H+I = O+10$ or $H+I+1 = O+10$. Either way, $H>O$ and $I>O$. Also, $L>O$.

This means that $H > 1$, $I > 0$, $L > 0$, and $O < 7$

Answer

Placing these conditions in several iterated loops, I received two solutions.

$68332 + 61547829 = 61616161$

and

$84661 + 80723419 = 80808080$

Rohan Lewis

2021.12.27

Code can be found here.