Sunday, 19 February 2012

Women Or Tigers? — Solution to Sixth Challenge

A bit more tricky, or at least time-consuming, yesterday’s challenge, wasn’t it?

The solution is that the woman is in Room I and the tiger in Room II. This is the only combination that fits with the signs on the doors and the conditions given as to whether they tell the truth or not.

But let’s look at the different possibilities in detail anyway.

If the woman is in Room I, that sign tells the truth, meaning that Room III is empty. The tiger must thus be in Room II, which fits with the sign on that door telling a lie.

This already rules out the second of second possibility, which would be a woman in Room I, an empty Room II, and a tiger in Room III — ‘cause then the sign on Room I would lie and cannot contain the woman.

If the tiger is in Room I, this sign is lying, meaning that the woman would be in Room III. She cannot be, as the sign on her door must tell the truth. (And, just for the thought experiment, if instead Room III is empty, the sign on the tiger’s door would not be lying as it is supposed to.)

Leaves us two theoretical possibilities, both implying that Room I is empty. As the sign on the empty room can both tell the truth or a lie, we have to move on to assumptions about who or what is in Room II. If it’s the woman, the sign on her room tells the truth …but it doesn’t, as Room I cannot both be empty and contain the tiger.

If instead the tiger is in Room II, it fits that that sign is lying. It leaves Room III for the woman …but that sign says the room is empty, which is a lie.

Therefore, the only valid possibility is the first one: Woman in I, tiger in II, and Room III is empty. The sixth prisoner can walk away a happy man with his new bride!

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