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Junior Mathematical Olympiad, September, 2019

Algebra Difficulty 2.2 Junior Find the answer Netherlands

In the puzzle below, $a, b, c, d$ , and $e$ are nonzero digits such that the two calculations are correct. The digits need not be distinct.
How many solutions are there for which $a < b$ ?

$ab \times ab = cde \quad \text{and} \quad ba \times ba = edc.$

A) 1 B) 2 C) 3 D) 4 E) 5

This was a multiple-choice question, but the options didn't survive into the source we have. The answer given is B, and the solution below works it through.

Solution

B) 2

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.