The words PULL and PUSH were painted on opposite sites of the door.

1. b8=N! Kxe8 2. Qg8#

If he runs toward the train, he’ll cover the remaining 3/7 of the trestle and meet the train at the far end. This means that if he runs away from the train, he’ll have covered 3/7 of the trestle (with 1/7 to go) when the train reaches the far end. He’ll then run the remaining 1/7 while the locomotive crosses all 7/7 and passes him. So the train is traveling at 7 times his speed, or 140 kph.

The waitress has asked, “Do you all want coffee?” In saying “I don’t know,” each of the first five logicians is saying, “I want coffee, and at this moment it does appear possible that all six of us do, but we don’t yet have enough information to say so definitively.”

The sixth logician doesn’t want coffee, so he’s able to say for certain that not everyone in the group does. So the waitress serves coffee to the first five logicians.

Yes. He puts on both pairs of gloves and performs the first operation. He puts aside the outer pair of gloves and performs the second operation. Then he turns the first pair inside out and puts them on over the now-used second pair. This puts the two non-sterile sides in contact while keeping his hands in their sterile state and making the remaining sterile side (formerly the inside) of the first pair of gloves available for use in the third operation.

If there were no ties, then Andy’s 6 scissors used up all of Bob’s non-scissors plays (2 rocks and 4 paper). That means that Bob’s remaining plays, 4 scissors, were used against Andy’s 3 rocks and 1 paper:

Andy won.

(By Yoshinao Katagiri, via Nob Yoshigahara.)

1. Qd6! and mate follows.

Let P be the number of pennies, D the number of dimes, and H the number of half dollars.

P + D + H = 100

and

P + 10D + 50H = 500,

so

9D + 49H = 400.

Now, we know that H is less than 10, and the only value for which (400 – 49H) is divisible by 9 is 1. So the totals are 1 half dollar, 39 dimes, and 60 pennies.

“If you take care of your peonies,” wrote Franklin P. Adams, “the dahlias will look after themselves.”

1. Second place.
2. $20.
3. February in a leap year.
4. S. (They’re the initial letters of the question.)
5. They were the same man, Grover Cleveland.

A full house with three aces will beat any other full house dealt in this hand, because only one hand can have three aces, assuming no cards are wild. But even this can still lose to a superior hand — four of a kind or a straight flush.

There’s nothing we can do to reduce the possibility that another player holds four of a kind — if we’re holding a full house then 11 varieties are possible. But by choosing carefully we can minimize the likelihood of a straight flush. Specifically, each of the hands AAA99, AAA88, AAA77, and AAA66 will prevent 13 straight flushes — each ace prevents one, and each spot card prevents five.

These are thus the best to choose; of the 40 possible straight flushes, each leaves only 40 – 13 = 27 straight flushes that can beat us. By contrast, the impressive-looking AAAKK leaves 40 – 6 = 34, or even more if we haven’t covered all four suits.

From Aaron Friedland’s Puzzles in Math and Logic, via Peter Winkler’s Mathematical Mind-Benders.