**From New Scientist #2551, 13th May 2006**

For homework Penny had to make an icosahedron from 20 equilateral triangles. Each triangle had to be numbered 1, 2, 3, 4 or 5 and at each vertex of the icosahedron the five triangular faces that met there all had to be different numbers.

Joe and Penny each made a model satisfying these requirements and in both cases the faces round the “top” vertex were 1 2 3 4 & 5 clockwise.

Although the overall arrangements of the numbers were different for both models, the orders of the numbers around the “bottom” vertex (diametrically opposite the top vertex) were the same.

Looking at the bottom vertex, what was that order, clockwise starting at 1?

[enigma1391]

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Solution:The numbers surrounding the bottom vertex are: 1, 5, 4, 3, 2 (in clockwise order).