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

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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 that 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, dropping the measurement by two paces every second anticlockwise 90 degree turn. 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?

posted Jul 17, 2019

Total area of the path is equal to the area of 100x100, width of the path is 2 paces, so the length is = 100*100/2=5000 paces

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