Answers to Five Puzzles

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1. Let's arbitrarily call the diamonds A, B, C. Put diamond A one side of the scale and B on the other. If the A side goes down, A is the odd one. If the B side goes down, B is the odd one. If they balance, C is the one.

2. Let's arbitrarily call the diamonds A, B, C. Put diamond A on one side of the scale and B on the other. If they balance, C is the odd diamond. Now put C on one side, A on the other. If C goes down, it's heavier; if it goes up, it's lighter.

Let's say that A and B don't balance and that A goes down. So either A or B are the odd ones. Now place A on one side, C on the other. If they are equal, B is it, and it's lighter. If A is heavier, A is it, and it's heavier.

3. Both pictures can be seen, with some effort, as two things. The one on the left, if the white is seen as the background, shows the faces of two people looking at each other. If the black is seen as the background, the white is seen as a vase. The one on the right (Frame C to the right) is more complicated, and can be seen as a young lady (Frame B) or as an old lady (Frame A), hence its famous name: "the young lady and the hag." haganswe.JPG (134009 bytes)

4. This is a classical example of a verbal dispute. There is no argument about facts, for they all agree on what's going on. There is no argument about attitude or emotions either, for this is really a neutral, non-ideological issue. So what are they arguing about? They argue about the meaning of going around. This expression has two meanings, as William James explains, the choice of starting point and direction is arbitrary): (i) Facing object X, then moving to the right of X, to its back, to its left, and to its front again. (ii) Moving from the north of X, to its east, south, west, and north again. Now, under normal circumstances, when we go around something, we conform to both (i) and (ii). But the problem presents an unusual circumstance where the man does (ii) but not (i). Once all this is clear, the argument, such as it is, evaporates; this dispute does not concern the real world, only the meaning of going around. If we had two different words for meanings (i) and (ii), there would have been no dispute.

5. Pour the liquid from cup #4 to cup #1, then return cup #4 to its place.

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