A problem posed by Harry Houdini: Given a piece of cardboard measuring 4″ × 2.5″, cut it so that a person can pass completely through it without tearing it.
Can it be done?
From the American journal Scripta Mathematica:
An elementary school teacher in New York state had her purse stolen. The thief had to be Lilian, Judy, David, Theo, or Margaret. When questioned, each child made three statements:
(1) I didn’t take the purse.
(2) I have never in my life stolen anything.
(3) Theo did it.
(4) I didn’t take the purse.
(5) My daddy is rich enough, and I have a purse of my own.
(6) Margaret knows who did it.
(7) I didn’t take the purse.
(8) I didn’t know Margaret before I enrolled in this school.
(9) Theo did it.
(10) I am not guilty.
(11) Margaret did it.
(12) Lillian is lying when she says I stole the purse.
(13) I didn’t take the teacher’s purse.
(14) Judy is guilty.
(15) David can vouch for me because he has known me since I was born.
Later, each child admitted that two of his statements were true and one was false. Assuming this is true, who stole the purse?
Is it possible to move the knight from a1 to h8, visiting every square of the chessboard once?
- Which is worth more, a pound of $10 gold pieces or half a pound of $20 gold pieces?
- A kazoo costs $1 plus half its price. How much does it cost?
- On its March 1961 cover, MAD Magazine pointed out that 1961 was the first “upside-up” year — the first year that reads the same upside down — since 1881. What will be the next such year?
Andrea’s only timepiece is a clock that’s fixed to the wall. One day she forgets to wind it and it stops.
She travels across town to have dinner with a friend whose own clock is always correct. When she returns home, she makes a simple calculation and sets her own clock accurately.
How does she manage this without knowing the travel time between her house and her friend’s?
You’re given a choice between two gifts: $5 and $1,000. You can choose either, but a bystander will give you $1 million if you choose irrationally. Can you do it?
See also Kavka’s Toxin Puzzle.
What do these words have in common?
A Christmas puzzle by J.C.J. Wainwright, from the American Chess Bulletin, December 1917.
White to mate in one move.
A woman visits a jewelry store and buys a ring for $100.
The next day she returns and asks to exchange it for another. She picks out one worth $200, thanks the jeweler and turns to go.
“Wait, miss,” he says. “That’s a $200 ring.”
“Yes,” she says. “I paid you $100 yesterday, and I’ve just given you a ring worth $100.”
And she trips lightly out of the store.
What do these words have in common?
It’s your first day at XYZ Industries, and your new boss calls you into his office. There you meet another trainee, J. Wellington Smithersby-Farquhar VII, the owner’s son, who is already helping himself to the brandy.
“Gentlemen,” says the boss, “we have a bit of a difficulty. You’ll both be starting at $100,000 per year, as promised. But I must offer you different increases. One of you will get a $15,000 raise each year, and the other a $5,000 raise every half-year.”
“That’s no problem, sir,” says Wellington, lighting a cigar. “I’m sure Jenkins will be quite happy with the smaller sum.”
The boss coughs uncomfortably. “Jenkins,” he says, “is that acceptable?”
How should you respond?
You’re a knight in love with a princess. Unfortunately, the king knows you’re poor and disapproves of the match.
On the night of a great feast, the king calls you up before his men and presents a golden box. In it are two folded slips of paper. One, he announces, reads “Marriage,” the other “Death.” “Choose one,” he says.
Pretending to stir the fire, the princess manages to whisper that both slips say “Death.” But the king and his men are waiting, and you cannot escape now.
What should you do?
Worshipful natives are rolling a giant statue of me across their island. The statue rests on a slab, which rests on rollers that have a circumference of 1 meter each. How far forward will the slab have moved when the rollers have made 1 revolution?
White to mate on the move.
“A real-right-down regular rare one. The problem exhibited is quite correct Chess, and no violation of any law takes place. In fact, it is found to be quite easy — when you know how.”
Here’s a curious way to multiply two numbers. Suppose we want to multiply 97 by 23. Write each at the head of a column. Now halve the first number successively, discarding remainders, until you reach 1, and double the second number correspondingly in its own column:
Cross out each row that has an even number in the left column, and add the numbers that remain in the second column:
That gives the right answer (97 × 23 = 2231). Why does it work?
One summer evening, as I was walking in the fields, I heard somebody behind me calling out my name. I turned round, and saw a friend of mine, at the distance of 400 yards, approaching to join me. We each of us moved 200 yards, with our faces towards the other, in a direct line yet we were still 400 yards asunder. How could this be?
– The Nic-Nac; or, Oracle of Knowledge, Sept. 13, 1823
Northland and Southland were happy neighbors until yesterday, when Northland declared that a Southland dollar was to be worth only 90 Northland cents.
Not to be outdone, Southland declared that a Northland dollar would be worth 90 Southland cents.
I live in Centerville, on the border between the two countries. I go into a Northland store and buy a kazoo, which costs 10 cents. I pay for it with a Northland dollar and receive a Southland dollar as change.
Then I go across the street and enter a Southland store. There I buy a lemon, which also costs 10 cents. I pay for it with a Southland dollar and receive a Northland dollar as change.
When I get home I have my kazoo and lemon, for which it appears I’ve paid nothing. And each of the merchants has an additional 10 cents in his receipts.
So who paid for the kazoo and the lemon?
(From Eugene Northrop.)
From Henry Dudeney:
“Place six matches as shown, and then shift one match without touching the others so that the new arrangement shall represent an arithmetical fraction equal to 1. The match forming the horizontal fraction bar must not be the one moved.”
An island is a body of land surrounded by water, and a lake is a body of water surrounded by land.
Now suppose the northern hemisphere were all land, and the southern hemisphere water. Is one an island, or is the other a lake?
In 1980 the Educational Testing Service offered this question on an aptitude test:
In pyramids ABCD and EFGHI shown above, all faces except base FGHI are equilateral triangles of equal size. If face ABC were placed on face EFG so that the vertices of the triangles coincide, how many exposed faces would the resulting solid have?
(A) Five (B) Six (C) Seven (D) Eight (E) Nine
Which is correct?
You’re standing with your friends Val and Colin when a stranger approaches and shows you 16 cards:
A♥ Q♥ 4♥
J♠ 8♠ 7♠ 4♠ 3♠ 2♠
K♣ Q♣ 6♣ 5♣ 4♣
He shuffles the cards, selects one, and tells Val the card’s value and Colin the card’s color. Then he asks, “Do you know which card I have?”
Val says, “I don’t know what the card is.”
Colin says, “I knew that you didn’t know.”
Val says, “I know the card now.”
Colin says, “I know it too.”
What is the card?