## Brain-Teaser 478

**From The Sunday Times, 26th July 1970** [link]

Brian and Betty have a daughter, Moira, and this can be proved by addition where each letter is represented by a different digit:

BRIAN + BETTY = MOIRAThe sum of the individual digit values of

MOIRAgives her age. The age of her brother Robert is similarly obtained. The sum of the children’s ages is a perfect square.How old is Robert?

[teaser478]

## Jim Randell 2:14 pm

on4 May 2019 Permalink |Once we have the solved the alphametic sum the value of ROBERT is determined.

We can use the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary to solve this puzzle.The following run file executes in 1.24s.

But it is faster to write a short program that uses the [[

`SubstitutedSum()`

]] solver.This Python program runs in 101ms.

Run:[ @repl.it ]Solution:Robert is 23.Moira is 26. Together the ages sum to 49 (= 7²).

There are 2 possible sums as the values of N and Y (in the units column of the sum) are interchangeable.

So the sum is one of:

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## GeoffR 3:10 pm

on6 May 2019 Permalink |The parents ages (22 and 13) or (23 and 12) don’t seem to make much sense in relation to the children’s ages! ie Robert (23) and Moira(26)

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