I want to mail a necklace to my wife, but anything sent through the mail will be stolen unless it’s sent in a padlocked box. A box can bear any number of padlocks, but neither of us has the key to a lock owned by the other. How can I mail the necklace safely to my wife?
A rope is passed over a pulley. It has a weight at one end and a monkey at the other. There is the same length of rope on either side and equilibrium is maintained. The rope weighs four ounces per foot. The age of the monkey and the age of the monkey’s mother together total four years. The weight of the monkey is as many pounds as the monkey’s mother is years old. The monkey’s mother is twice as old as the monkey was when the monkey’s mother was half as old as the monkey will be when the monkey is three times as old as the monkey’s mother was when the monkey’s mother was three times as old as the monkey. The weight of the rope and the weight at the end is half as much again as the difference in weight between the weight of the weight and the weight and the weight of the monkey. Now, what is the length of the rope?
A conundrum from Henry Ernest Dudeney, Modern Puzzles, 1926:
Dora Crackham one morning produced a slip of paper bearing the jumble of figures shown in our illustration. She said that a young mathematician had this poser presented to him by his betrothed when she was in a playful mood.
“What am I to do with it?” asked George.
“Just interpret its meaning,” she replied. “If it is properly regarded it should not be difficult to decipher.”
What did she mean?
I’ll give you a million dollars if you intend to drink this poison.
You don’t actually have to drink it. I’ll pay you immediately, and then you’re perfectly free to change your mind.
Can you do this?
(Posed by University of California political philosopher Gregory Kavka.)
Vladimir Nabokov composed chess problems. Here’s a clever one from 1932: “White retracts its last move and mates in one.”
This is an instance of retrograde analysis: Of the many legal moves that White might just have made, only one can be revised to yield an immediate mate. Can you find it?
Twenty-five ants are placed randomly on a meter stick. Each faces east or west. At a signal they all start to march at 1 centimeter per second. Whenever two ants collide they reverse directions. How long must we wait to be sure that all the ants have left the stick?
This sounds immensely complicated, but with a simple insight the answer is immediately clear. What is it?
What English word contains the letters GNT consecutively?
Given any pair of potatoes — even bizarre, Richard Nixon-shaped potatoes — it’s always possible to draw a loop on each so that the two loops are identical in three dimensions.
Do you see the simple, intuitive proof for this?
I show you three cards. One is white on both sides, one is black on both sides, and one is white on one side and black on the other. I shake them in a hat, remove one at random, and place it on a table. The side that’s face up is black. What’s the probability that the other side is also black?
Hint: It’s not 1/2.
In his almanac, Ben Franklin made some alarming predictions for the year 1736: He said that the sea would rise and put New York and Boston under water, and that American vessels would be taken out of port “by a power with which we are not now at war.”
A year later he announced he’d been right: Seawater evaporates and descends as rain, and we are not at war with the wind.
