**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.

[enigma73]

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This program examines all possible quartet values and comes up with the solution in 1m36s (using PyPy), so it’s not particularly quick, or particularly elegant.

Solution:The minimal third-greatest quartet number is 24.I augmented the code to count the number of solutions and it found 192.

One way to achieve the solution is shown below:

Where are the attorneys of the New Scientist Magazine?

Why don’t they interfere with those fake inventors?

Jim : I’d like to thank you for bringing this example of the grid and node playboard to light. I’ve not come across this before, and it shows that, as the saying goes, “there is nothing new under the sun”.

I would like to point out, however, that though the playboard is the same as that used for Sujiko, the puzzle itself differs greatly, as does the method of play, and far from being a “fake inventor”, I believe that I created a puzzle which not only differs from this example, but also from all others which were in circulation in 2010.