# Sunday Times Teaser 3088 – Bog Standard Deviation

*by Stephen Hogg*

#### Published Sunday November 28 2021 (link)

My four toilet rolls had zigzag-cut remnants (not unlike that shown). Curiously, each polygonal remnant had a different two-figure prime number of sides, each with a digit sum itself prime.

Calculating the average number of sides for the four remnants and the average of their squares, I found that the average of the squares minus the square of the average had a value whose square root (the “standard deviation”) was a whole number.

I also noticed that a regular convex polygon with a number of sides equal to the average number of sides would have an odd whole-number internal angle (in degrees).

Give the “standard deviation”.

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This solution works ‘backwards’ starting with the internal angles of regular polygons

This version starts from the four ‘special’ prime sequences.