Brain Teasers
King's Path
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?
Answer
The path was 5000 paces long. If the path is straightened out into a line, its area is that of the square, 100x100 square paces. Dividing by the path width 2 gives the solution.Hide Answer Show Answer
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Comments
I said 1 less pace than the answer given. I assumed that the king wouldn't take the last step into the bushes!
Actually, I used excel, figured that he'd walk 99,99,99, then 97,97 and 95,95 and so on until he walked 1,1. Adding them up gave 5099. He's going to walk 99 paces for the first three walks, and then it'll get shorter. Remember he's walking in the middle of the path, not the inside or outside edge...
Daze into Knights ! Lol that was more fun than the actual teaser. well done!
Good puzzle. I was surprised to find the provided answer was the same as the method I had used. To the skeptics, its easy to verify the method by modeling it with a 2 x 2 square in which the king would walk 1.5 + 1 + 1.5 = 4 paces.
Sorry 4 x 4 square because the path has to be 2 m wide so 4 x 4 / 2= 8. The king walks 3 + 2 + 3 = 8. The principal is the same as a 2 x2 square with a 1 metre wide path.
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