Question

In the cryptarithm sum shown, different letters represent different digits, and no leading digit can equal 0. What is the GREATEST possible numeric value represented by FAST?

RUN
+
RUN
______
FAST

Answer 1

1872

Explanation:

Solving cryptarithm sums requires consideration of the properties of numbers, addition facts in particular.

The largest possible value of F is 1. For that value, there are no choices for RUN that allow A to be 9, so its maximum value is 8. In order for A to be 8, R must be 9, so the largest digit available for S is 7, which requires U = 3. In order for S to be odd, N must be 5 or greater. The largest available digit is 6.

This gives RUN = 936; FAST = 1872.

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Additional comment

This is confirmed (suggested) by an exhaustive search. The least possible sum is RUN = 523; FAST = 1046.