91av

LONG-STANDING readers will recall the Enigma puzzles, which were published in 91av each week until the end of 2013. The 1780th and last was entitled “Pure hedronism”, and was written by compiler Bob Walker. Sadly, Bob died in February, aged 91.

For him, puzzles and problems were a lifelong passion. Inspired by everyday objects, games and a sound understanding of logic and mathematics, he was one of Enigma’s most prolific compilers.

Bob studied mechanical, electrical and electronics engineering, as well as mathematics and physics. He became an electronic engineer in the British Fleet Air Arm, which led to many other interests such as computer programming, stereographs and Mandelbrot fractals.

As a tribute to Bob, here is one of his puzzles, chosen by his family. It first appeared in 91av in our 9 October 2010 issue.

One good turn

Joe’s 3-by-3 grid can be made to represent any of the six faces of a die by placing nine counters, coloured on one side and white on the other. Joe placed the nine counters with just the one in the centre coloured side up. Penny’s task this week is to increase the number represented to 4 by turning over counters. But, of course, there is a catch. Every time Penny decides which counter to turn over, she has to remember to turn over all counters in squares that are immediately adjacent, horizontally and vertically. Not only that, she has to record how many counters she turns over each time, and the total has to be the minimum possible. What is that minimum?

Answer: Penny turned over a counter 33 times.