# Messy order | Science | THE COUNTRY

The solution to the "problem of the happy ending", raised last week, is 5. To see it more clearly, instead of stars consider 5 nails nailed halfway in a flat board: if we surround them with a loop and tighten it around the set until the string is taut, there are three possibilities: the string It forms a pentagon with the 5 nails as vertices, the string forms a quadrilateral with 4 nails as vertices and 1 inside, the string forms a triangle with 3 of the nails as vertices and 2 inside. In the first case, any 4 of the nails form a convex quadrilateral; in the second case, we already have the quadrilateral; and in the third, the 2 inner nails form a convex quadrilateral with 2 of the triangle. The attached illustration (taken from Clara Grima's article cited last week) shows it clearly.

### Primity and divisibility

We can know if a number, however long, is divisible by 5 without more than seeing its last figure: if it is a 0 or a 5, the number will be divisible by 5; otherwise, it will not be

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