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?
Puzzles
The Three Cards Problem
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.
“Enigmatical Prophecies”
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.
The Apple Conundrum
Two women are selling apples. The first sells 30 apples at 2 for $1, earning $15. The second sells 30 apples at 3 for $1, earning $10. So between them they’ve sold 60 apples for $25.
The next day they set the same goal but work together. They sell 60 apples at 5 for $2, but they’re puzzled to find that they’ve made only $24.
What became of the other dollar?
Stumper
Plutarch wrote that Homer died of exasperation because he couldn’t solve a fisherman’s riddle:
“What we have caught we threw away; what we could not catch we kept.”
The answer is “fleas.”
Setup Job
From Henry Ernest Dudeney, Amusements in Mathematics (1917):
I have a single chessboard and a single set of chessmen. In how many different ways may the men be correctly set up for the beginning of a game? I find that most people slip at a particular point in making the calculation.
Where’s the Error?
A man deposited $50 in a savings account, then withdrew it in various sums. When he’d recovered his $50 he was surprised to find $1 left in the account, though it had drawn no interest. When he inquired, the bank produced this ledger:
Menagerie
This 1872 Currier and Ives print is titled The Puzzled Fox: Find the Horse, Lamb, Wild Boar, Men’s and Women’s Faces. There are eight human and animal faces hidden in the scene. Can you find them?
Ironically, the birds that are visible have now disappeared — they’re passenger pigeons.
Island Livestock
What’s remarkable about this sentence, composed by Dmitri Borgmann?
IN JULY, OH MY KILLJOY MOLLY, I’LL LOOK IN UPON MY JUMPY POLO PONY UP IN HILLY HONOLULU.
Trevanion’s Escape
Confined in Colchester Castle during the English civil war, the royalist officer Sir John Trevanion was awaiting execution when he received this letter:
Worthie Sir John:- Hope, that is ye beste comfort of ye afflicted, cannot much, I fear me, help you now. That I would saye to you, is this only: if ever I may be able to requite that I do owe you, stand not upon asking me. ‘Tis not much that I can do: but what I can do, bee ye verie sure I wille. I knowe that, if dethe comes, if ordinary men fear it, it frights not you, accounting it for a high honor, to have such a rewarde of your loyalty. Pray yet that you may be spared this soe bitter, cup. I fear not that you will grudge any sufferings; only if bie submission you can turn them away, ’tis the part of a wise man. Tell me, an if you can, to do for you anythinge that you wolde have done. The general goes back on Wednesday. Restinge your servant to command. — R.T.
Sir John studied the message for several hours, and then, apparently despairing, asked to spend some time alone in prayer. His captors agreed — and never saw him again.
Read the third letter after each punctuation mark.