1. Ng3 Kb3 2. Rh1 Ka3 3. Ng1 Kb3 4. Rf3 Ka3 5. Bf2 Kb3 6. Re3 Ka3 7. Nf3 Kb3 8. Rg1 Ka3 9. Nh1 Kb3 10. Bg3 Ka3 11. Nf2 Kb3 12. Rh1 Ka3 13. Ng1 Kb3 14. Rf3 Ka3 15. Ke3 Kb3 16. Nd3 Ka3 17. Kf2 Kb3 18. Re3 Ka3 19. Kf3 Kb3 20. Nf2 Ka3 21. Rxc3#

(Thanks to Matt for this solution.)

At least one of the books must be entirely blank, about nothing.

Or, as someone just wrote to me, “It’s about things that men know about women.”

From Robert Morrison Abraham, Diversions and Pastimes, 1935.

The camper reached a point 3 2/3 miles from his camp. First he paddled upstream at a net rate of 2.5 mph for 48 minutes and thus met the bottle at a point 2 miles above camp. From that point the bottle took 80 minutes to float down to camp. The canoeist spent half that time paddling upstream and half downstream (the two times must be equal). In 40 minutes paddling upstream he traveled another 1 2/3 miles, for a total of 3 2/3 miles.

A simple way to see why the 80 minutes must be halved is to imagine that we can turn off the river’s current. In that case the canoeist is simply paddling at a steady rate away from the bottle and back to it.

Call a person an Odd if he has shaken hands an odd number of times (at any given moment). An Even has shaken hands an even number of times.

At the start, the number of Odds is zero, an even number. As the evening progresses, three types of handshake take place:

1. An Odd shakes with an Odd. In this case they both become Evens; the total number of Odds decreases by 2.
2. An Even shakes with an Even. Both become Odds, and the number of Odds increases by 2.
3. An Even shakes with an Odd. The Even becomes an Odd, and the Odd becomes an Even, so the total number of Odds remains unchanged.

Because the number of Odds can change only by an even number, the number of people who have shaken hands an odd number of times remains even — not only at the end of the evening, but at every moment throughout!

A Norwegian reader adds: “It might possibly be of some minor interest that in Norway, Odd and Even are both widespread men’s names. Fittingly, as of the most recently updated name statistics (2009), there are 22821 Norwegian men with Odd as their first first name, and 5846 with Even as their first first name. (And 29 are called Odd Even.)”

1. Qe4 and White wins by 2. Qxe5#, 2. c5#, 2. Qg6#, or 2. Qxd5#.

From Charles F. Stubbs, Canadian Chess Problems, 1890.

The first player must place his first cigar on end in the exact centre of the table, as indicated by the little circle. Now, whatever the second player may do throughout, the first player must always repeat it in an exactly diametrically opposite position. Thus, if the second player places a cigar at A, I put one at AA; he places one at B, I put one at BB; he places one at C, I put one at CC; he places one at D, I put one at DD; he places one at E, I put one at EE; and so on until no more cigars can be placed without touching.

“I smoke ten to fifteen cigars a day,” said George Burns. “At my age I have to hold on to something.”

Perhaps surprisingly, the potatoes now weigh 50 pounds. The sack of potatoes originally weighed 100 pounds, and 1 percent of its weight, or 1 pound, was non-water. If that 1 pound now makes up 2 percent of the total weight, then the total weight must be 50 pounds.

Not a paradox, exactly, but many people find it counterintuitive.

1. Qa8! and Black must succumb to a check from a8, h8, or h6.

Alexander will win again. We know that Alexander covers 100 meters in the time it takes Zachary to cover 97. If Alexander starts 3 meters behind the starting line, then the two brothers will be neck and neck at the 97-meter mark, and Alexander will pull ahead.