# Sunday Times Teaser 3181 – “No slack, Alice!” says Grace

*by Stephen Hogg*

#### Published Sunday September 10 2023 (link)

Grace mimicked Mr Dodgson: ‘’Take two different positive odd numbers with no shared prime factor. Multiply the larger by their sum, giving the perimeter of a distinct right-angled triangle with whole-number sides. Only such values and their multiples work.’’

Alice created a loop from part of a 1m thread. She was able to pull it tightly on a pinboard into a right-angled triangle with whole-number cm sides in two ways (with different-shaped triangles).

Alice then pulled the same loop tight over the thin polar spike of the classroom globe, down two meridians and along the equator. Thinking ‘’Logic’s dead!’’, she saw 90° equatorial angles and a non-zero polar angle, which obviously didn’t add to 180°.

Grace calculated the polar angle to the nearest degree. Curiously, transposing its two digits gave the globe’s whole-number centimetre radius.

Give this radius

Using Dr Dodgson’s method:

I also produced a version using Dr Dodgson’s method: