## Teaser 2840: Signs of the times

**From The Sunday Times, 26th February 2017** [link]

I was taking a gentle morning drive along the straight road to Secombe that passes through Firsk. Before reaching Firsk I passed three signposts, each giving the distances to Firsk and to Secombe (to the nearest mile). All six distances displayed were different and, amazingly, all were perfect squares [less than 100].

What were the two distances given on the first signpost (furthest from Firsk)?

I have added the “less than 100” condition to reduce ambiguity in the puzzle.

[teaser2840]

## Jim Randell 9:54 am

on4 October 2019 Permalink |When this puzzle was first published there was some confusion over the correct interpretation. I have added the condition to require the squares to be less than 100 to eliminate multiple solutions.

The distances on the signposts are rounded to the nearest mile. This Python program uses intervals to find viable solutions. It runs in 47ms.

Run:[ @repl.it ]Solution:The distances on the first signpost encountered were 49 miles (to Firsk) and 64 miles (to Secombe).The distance between F and S is between 15 and 16 miles.

So if, for example, the distance between F and S was 15.2 miles, and the signposts are at distances of 1.2 miles, 9.4 miles and 48.6 miles from F, then they would read:

Without the restriction on the squares there are further solutions that use distances of 100 and 121 (and higher values):

And with even higher values we can solve the puzzle using exact distances:

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