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MathNet 2019-part-04 — 184 problems (EN–VI) Question 65

Math Olympiad Vault · MathNet 2019-part-04 — 184 problems (EN–VI)

Question 65

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 $a \lt b$?

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

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