The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.


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Submitted by Mihai Basa:

Once upon a time, there was a wise Shah that ruled on a mountain. He wanted to have a castle built, but didn't want to spend too much of his (beloved) people's money on it. So he decided it should have five walls and ten towers, with exactly four towers on each wall. A tower could (as all good architects know) only be built on an intersection or corner formed by two walls. He told this exact request to his chief architect. After one long night of frowning and pondering his architect returned with a plan for the castle. It looked like this:

The king looked at it, nodded, and then said: Yes, this is what I asked you for. But, you see, I've thought better about things and have decided that we need to make a modification. In case of a siege I need a place to rest, away from the noise of fighting: I need a tower for myself, completely enclosed by walls. All the other conditions can stay the same.

The architect sighed, picked up his papers and left. After another long night of scribbling little lines and dots, the architect returned with a plan to satisfy the king's new request. When he showed it to the king it looked like this:

The king looked at it for a long time, and finally said: My dear architect, you know how highly I value your work - you are the best architect Puzzlania has seen for many generations... But I must refuse this plan as well. You see, my wife deserves to have a place to rest of her own, a quiet place, preferably not far away from me, either. I must ask that you somehow manage to put two towers inside the castle walls, without breaking any of the general rules I told you two days ago. The architect turned pale, mumbled something about 'impossibilities are impossibilities', took his papers and left with only the quickest bow towards the king. One more tedious night of thought and trial passed, but the next day the architect had found the solution to the king's request.

What was his solution?

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