Enigma 1475: Lines of thought
9 December 2012
Posted by on
From New Scientist #2637, 5th January 2008
Joe cut out a number of small square cards. On some of them he drew a thin red line joining the centres of two opposite sides and on the others he drew a thin red line joining the centres of two adjacent sides.
Penny’s challenge was to select 24 cards and arrange them in a 6-card by 4-card rectangle so as to produce a number of small areas, each with a complete single boundary of thin red lines, with a total area equal to five-sixteenths of the total card area.
Penny could choose any combination of cards – for example, 10 of the first and 14 of the second – but only some of the combinations would lead to her meeting the challenge.
How many of the combinations?