Library / UKMT Intermediate Mathematical Challenge /134 of 267

UKMT Intermediate Mathematical Challenge, 2018

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

How many two-digit squares have the property that the product of their digits is also a square?

(A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) $4$

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.