King-size Conundrum

A medieval king needed to work out how he could recruit fighting men for the battle ahead. However, there were so many distractions around the castle, his thinking became confused. So in order to change his daze into knights, he asked for a secluded walk to be made so he could ponder in peace.

The head gardener was given the job of planting lines of high bushes. First, he planted a line running 100 paces east. Then from the end of that line he planted a line 100 paces north, then 100 west, 98 south, 98 east, 96 north, 96 west, and so on. This made a square spiral path 2 paces wide.

If the king intended to walk down the middle of the path, how long was the path?


The path was 5000 paces long.

If the path is straightened out into a line, its area equals the area of the whole square, that is, 100 x 100 square paces. Dividing the result by the width of the path gives the length (or the solution).

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