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”.