# Sunday Times Teaser 3134 – Stringing Along

*by Peter Good*

#### Published Sunday October 16 2022 (link)

An artist hammered thin nails from a pack of 40 into a board to form the perimeter of a rectangle with a 1cm gap between adjacent nails. He created a work of art by stringing a long piece of wire from one nail to another, such that no section of wire was parallel to an edge of the rectangle. The wire started and ended at two different nails, no nail was used more than once and the length of the wire was a whole number of cm. No longer wire was possible that satisfied the above conditions.

What were the dimensions of the rectangle and the length of the wire chain (in cm)?

Note: the original (later corrected) on-line version omitted the red text.

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I assumed that the wire length was an exact integer and that only some of the 40 pins are used.

Here is a picture of the solution: