**From New Scientist #1387, 8th December 1983** [link]

The picture shows a cuboctahedron, with 12 vertices lettered *A* to *L*, and 14 faces, of which six are squares and eight are triangles.

The problem is to place a different positive whole number so that the sum of the numbers at the corners of each square face is the same and the sum of the numbers at the corners of each triangular face is the same.

In doing so, first make the number at *A* as small as possible. Then make *B* as small as possible. Then *C* … and so on.

What numbers go at *I*, *J*, *K*, *L*?

[enigma241]

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Enigma 225 was about labelling the faces on a cuboctahedron.

This Python 3 program finds the best solution in 326ms.

Solution:I = 4; J = 5; K = 6; L = 13.The complete layout is as follows:

A = 1; B = 8; C = 9; D = 10; E = 12; F = 11; G = 3; H = 2; I = 4; J = 5; K = 6; L = 13;

The numbers on the red background label the vertices. The black numbers on the faces indicate the sum of the surrounding vertices.