One or none of the three signs tell the truth. Let’s assume that the one on Room I does tell the truth. That would mean there is a tiger in that room. It would also mean that the two other signs are both lying. For Room II that could fit, as it would hide a tiger. However, that would make the sign on Room III correct — so we can rule out that possibility.
So how about the sign on Room II… if it tells the truth, the two other signs do not… but the one on Room I should then contain a woman. As there is a woman in only one of the rooms, this possibility can be discarded as well.
Maybe the sign on Room III is correct, making the two others lie. That would mean there is a woman in Room I, a tiger in Room II, and as the signs do not give any indications of what is behind the third door, there could be a tiger. In other words, this could be a possibility.
Still, let’s check if all three signs are lying: Woman in Room I, tiger in Room II… but then the sign on Room III is not lying. So that one’s out as well.
The prisoner should open the door to Room I this time!
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