From New Scientist #1404, 5th April 1984 [link]
This is an easy introduction to Hexa-draughts, which is played on a board with a “hexagonal” pattern of points extending as far as you like in all directions.
First you place a number of men on points on or below Row 0. That is your start position. Then you hop, as in draughts: one man A hops over an adjacent man B, landing on the point beyond, and removing B from the board. And so on, till only one man is left, as far as possible above Row 0.
The picture shows a start position with three men — the fewest needed to get a man to row 2; so we say M(2) = 3. The numbers in the circles and the arrows on them show the order and direction of hops.
What is M(4)?
The setter added the following note:
If you find this interesting, you may like to seek M(5), M(6), and M(7). My best answers so far are 17, 38, and “probably impossible”. If you can do better, no prizes, but I should rather like to know M(8) is certainly impossible.
With this puzzle the prize offered for Enigma solutions was increased from £5 to £10.
When Enigma was launched the cover price of New Scientist was 35p, so the prize would buy 14.3 copies of the magazine. By 1984 the cover price of the magazine had risen to 90p, so the purchasing power of the £5 prize had dwindled to only 5.6 copies of the magazine. The increase of the prize to £10 brings it up to 11.1 copies.
At some point between 1996 and 2000 the prize was increased again to £15. When the final Enigma puzzle was published in 2013 the cover price of the magazine was £3.80 (actually the Christmas edition was £3.95), and the prize was £15, which would only buy 3.9 copies of the magazine. If the cover price to prize ratio from Enigma 1 had been maintained the prize would have been £55.