By J. Schumer, Transvaal Leader, 1906. White to mate in two moves.
Puzzle maven David Singmaster presented this conundrum at the first Gathering for Gardner:
My daughter Jessica is 16 and very conscious of her age. Our neighbour Helen is just 8, and I teased Jessica by saying, ‘Seven years ago, you were 9 times as old as Helen; six years ago, you were 5 times her age; four years ago, you were 3 times her age; and now you are only twice her age. If you are not careful, soon you’ll be the same age!’
Jessica seemed a bit worried, and went off muttering. I saw her doing a lot of scribbling.
The next day, she said to me, ‘Dad, that’s just the limit! By the way, did you ever consider when I would be half as old as Helen?’ Now it was my turn to be worried, and I began muttering — ‘That can’t be, you’re always older than Helen.’
‘Don’t be so positive,’ said Jessica, as she stomped off to school.
Can you help me out?
He withheld the answer, but I think I see it.
Jocasta Jones is walking in a wood when she discovers a deep freeze containing a man. She thaws him out, and he introduces himself as Dum and shows her a book that explains how to build a time machine and a deep freeze.
Jocasta and Dum marry and produce a baby, whom they name Dee. Dee grows up, discovers the book, builds a time machine and gets inside, taking his father and the book with him. The journey into the past takes a long time, and Dee is forced to kill and eat his father to stay alive.
Wracked with guilt, he emerges at his destination and destroys the machine. He changes his name to Dum, but still fearful of being punished, he builds a deep freeze and gets inside, taking the book with him. He is awakened by Jocasta.
Now, asks University of Nottingham philosopher Jonathan Harrison, “Did Jocasta commit a logically possible crime?” From her perspective, Dum enters her life, they have a child, and husband and child both disappear. But from Dee’s perspective, she has married her son and borne a child. Is this incest?
(Harrison, J. (1979) “Jocasta’s crime”, Analysis 39, 65.)
If we made a dictionary of all the integers, arranging their English names in alphabetical order, which would come first and which last?
A large rectangle is partitioned into smaller rectangles, each of which has either integer height or integer width (or both). Prove that the large rectangle itself must have integer height or integer width.
An amusement card from France, circa 1880. Where is the tiger?
By B. Harley and C.G. Watney, Good Companion, 1921. White to mate in two moves.
You’re about to roll five regular dice. Which is more likely, rolling no sixes or rolling exactly one six?
At age 10, Nob Yoshigahara won the grand prize in a newspaper competition with this puzzle:
Given a sack of sugar, an unbalanced scale, and two 5-pound weights, measure exactly 10 pounds of sugar.
A problem from Litton Problematical Recreations, which attributes it to Fermat circa 1635:
What is the remainder upon dividing 5999,999 by 7?
I place four balls in a hat: a blue one, a white one, and two red ones. Now I draw two balls, look at them, and announce that at least one of them is red. What is the chance that the other is red?
By O. Dehler, Tidskrift för Schack, 1928. White to mate in two moves.
My wife and I attend a party with four other couples. When we arrive there’s a certain amount of hand-shaking, but no one shakes his own hand and no husband shakes his wife’s hand. I ask the nine other guests how many hands each shook, and I get nine different answers. How many hands did my wife shake?
Using only a 4-minute hourglass and a 7-minute hourglass, how can you measure 9 minutes?
We’re playing Russian roulette. The revolver has six chambers, all empty. I put bullets in two adjacent chambers, spin the cylinder, hold the gun to my head, and pull the trigger. It clicks. Now it’s your turn. Before pulling the trigger, you can choose to spin the cylinder again or leave it as it is. Which is better?
Puzzle maven Noboyuki Yoshigahara noticed this sign on the glass door of an Osaka restaurant:
What is its meaning?
A man is 4/7 across a train trestle when he sees a train coming. To get off the trestle, he can run toward the train or away from it. As it happens, in either case he’ll reach safety just as the locomotive passes him. If he runs at 20 kph, how fast is the train going?
Six logicians finish dinner. The waitress asks, “Do you all want coffee?”
First logician: “I don’t know.”
Second logician: “I don’t know.”
Third logician: “I don’t know.”
Fourth logician: “I don’t know.”
Fifth logician: “I don’t know.”
Sixth logician: “No.”
Who gets coffee and why?
A surgeon wears sterile gloves both to protect his patient and to protect himself. Can a hard-pressed surgeon with only two pairs of sterile gloves operate on three patients while keeping everyone safe?
Andy and Bob play rock-paper-scissors 10 times. Andy plays 3 rocks, 6 scissors, and 1 paper (in some order), and Bob plays 2 rocks, 4 scissors, and 4 paper. There are no ties. Who wins?