Enigma 73: Quartetting
20 March 2013
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From New Scientist #1216, 28th August 1980 [link]
The quartet-numbers in the circles show the sums of the numbers in the four surrounding squares. The object is to arrange the numbers 1 to 9 in the squares so that the quartet-numbers, ignoring the two biggest ones, are as small as possible. The arrangement shown achieves a maximum quartet-number of 14, ignoring the two 26’s.
I ask you to arrange the numbers 1 to 16 in a 4 × 4 grid, so that the greatest of the nine quartet-numbers (ignoring the two biggest) is as small as possible. What is the least third-greatest quartet-number you can achieve? (The best pattern, I may add, is not unique).
This is somewhat similar to the Sujiko puzzles published in the Daily Telegraph, although those seem to have been “invented” in 2010, so this Enigma predates that by some 30 years.