1. A jeweler has 3 diamonds. They all look exactly
alike, but one diamond is heavier than the others. How can she identify the heavier
diamond by using a balance scale just once? Please outline your argument as carefully as
2. Same as above, but now the jeweler doesn't know whether the odd
diamond is lighter or heavier than the other two. By using the scale twice, how can she
tell (i) which is the odd one, and (ii) whether it is lighter or heavier?
3. What do you see in the two sketches below?
4. An unfinished story by William James is reprinted below. Please
think about James' predicament and come prepared to tell the class next session: Does the
man, or doesn't he, go round the squirrel?
Some year ago, being with a camping party in the mountains, I
returned from a solitary ramble to find every one engaged in a ferocious metaphysical
dispute. The corpus of the dispute was a squirrel--a live squirrel supposed to be clinging
to one side of a tree-trunk; while over against the tree's opposite side a human being was
imagined to stand. This human witness tries to get sight of the squirrel by moving rapidly
round the tree, but no matter how fast he goes, the squirrel moves as fast in the opposite
direction, and always keeps the tree between himself and the man, so that never a glimpse
of him is caught. The resultant metaphysical problem is this: Does the man go round the
squirrel or not? He goes round the tree, sure enough, and the squirrel is on the tree; but
does he go round the squirrel? In the unlimited leisure of the wilderness, discussion had
been worn threadbare. Everyone had taken sides, and was obstinate; and the numbers on both
sides were even. Each side, when I appeared, therefore appealed to me to make it a
majority. Mindful of the scholastic adage that whenever you meet a contradiction you must
make a distinction, I immediately sought and found one, as follows:
|5. Three glasses contain liquid, and three are empty. Rearrange the
glasses so that they alternate--one with liquid, one without, one with liquid, one
without, etc. You are allowed to touch or move only one glass.