Solutions to Brain-Twisters II
The solutions too will often involve the use of figures and tables. As in the puzzles page, the figures are in gif format and should be downloadable by text-based browsers like Lynx.
Since the signs say the same thing, they are both true or both false. Suppose they are true; then both rooms contain ladies. This would mean in particular that Room II contains a lady. But we have been told that if Room II contains a lady, the sign is false. This is a contradiction, so the signs are not true; they are both false. Therefore, Room I contains a tiger and Room II contains a lady, so you should choose Room II.
If Room I contains a tiger, we get a contradiction. Because if it does contain a tiger, then Sign I is false, which would mean that neither room contains a lady; both rooms would contain tigers. But a tiger in Room II would indicate that Sign II is true, which would mean that the other room contains a lady, contrary to the assumption that Room I contains a tiger. So it is impossible for Room I to contain a tiger; it must contain a lady. Therefore, what Sign II says is true, and Room II must contain a tiger. You should, therefore, choose Room I.
Sign I says, in effect, that either both rooms contain ladies or both contain tigers - that is the only way it could make no difference which room is picked.
Suppose Room I contains a lady. then Sign I is true, which means Room II also contains a lady. Suppose, on the other hand, Room I contains a tiger. Then Sign I is false, which means that the two occupants are not the same, so again the occupant of Room II is a lady. This proves that Room II must contain a lady regardless of what is in Room I. Since Room II contains a lady, Sign II is false and Room I must contain a tiger. You should, therefore, choose Room II.
Sign I says, in effect, that the two occupants are different (one a lady and the other a tiger), but doesn't say which room contains which. If the occupant of Room I is lady, Sign I true; hence Room II must contain a tiger. If, on the other hand, the occupant of Room I is a tiger, then Sign I is false, which means that the two occupants are not really different, so Room II must also contain a tiger. Therefore, Room II definitely contains a tiger. This means that Sign II is true , so a lady must be in Room I - the room you should choose.
Suppose the first sign, THIS ROOM CONTAINS A TIGER, is on the door of Room I. If a lady is in the room, the sign is false, violating the conditions given us. If a tiger is Room I, the sign is true, which again violates the conditions of the puzzle. Therefore, this sign can't be on the door of Room I; it must be on the door of Room II.
This means that the sign for Room I reads: BOTH ROOMS CONTAIN TIGERS. Then Room I can't contain a lady, or the sign would be true, which would mean that both rooms contain tigers - an obvious contradiction. Therefore, Room I contains a tiger. From this it follows that the sign is false, so Room II must contain a lady.
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Revised: August 29, 1996