Library / UKMT Junior Mathematical Challenge /187 of 274

UKMT Junior Mathematical Challenge, 2025

Algebra Difficulty 2.0 Junior Find the answer United Kingdom

In a sequence of rectangles, the first has height $10\text{ cm}$ and width $13\text{ cm}$ . Each of the following rectangles is $2\text{ cm}$ higher and $1\text{ cm}$ wider than the previous rectangle in the sequence. How many rectangles in this sequence are also squares?

(A) $0$ (B) $1$ (C) $2$ (D) $4$ (E) an infinite number

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.