“A Crime Story”

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:

Lilian:
(1) I didn’t take the purse.
(2) I have never in my life stolen anything.
(3) Theo did it.

Judy:
(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.

David:
(7) I didn’t take the purse.
(8) I didn’t know Margaret before I enrolled in this school.
(9) Theo did it.

Theo:
(10) I am not guilty.
(11) Margaret did it.
(12) Lillian is lying when she says I stole the purse.

Margaret:
(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?

	Select Click for Answer
Theo is innocent because he says so twice. Then (9) is a lie. Since (9) is a lie, (8) is true. Since (8) is true, (15) is a lie. Since (15) is a lie, (14) is true. Judy is the thief.

November 11, 2009January 22, 2013 | Puzzles

A Riding Tour

a riding tour

Is it possible to move the knight from a1 to h8, visiting every square of the chessboard once?

	Select Click for Answer
No. A knight lands on light and dark squares alternately. If it begins on a dark square and makes 63 moves, then the last move must end on a light square. h8 is dark. Therefore the task is impossible. For the same reason, the task is also impossible to a rook.

November 8, 2009January 22, 2013 | Puzzles

Misc

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?

	Select Click for Answer
The first. A pound of gold is worth more than half a pound. $2. 6009.

November 5, 2009January 22, 2013 | Puzzles

The Stopped Clock

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?

	Select Click for Answer
Before she leaves the house, Andrea winds her own clock and sets it to an arbitrary time. Then she notes the correct time at her friend’s house both when she arrives and when she leaves. When she returns home she consults her own clock to see how much time the whole trip has taken, subtracts the period she spent at her friend’s house, and divides the result by two to learn the travel time in each direction. By adding this interval to the time she noted as she left her friend’s house, she can infer the current time and set her own clock.

Click for Answer

October 31, 2009August 11, 2013 | Puzzles

Dilemma

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?

Find the Theme, Part 2

What do these words have in common?

ALMOND
INCOME
CANDID
MEMORIAL
CONCORDE
GANYMEDE
MANDARIN
MAINLAND

	Select Click for Answer
All are composed of U.S. state postal abbreviations.

October 9, 2009January 22, 2013 | Puzzles

Hell’s Bells

hell's bells

A Christmas puzzle by J.C.J. Wainwright, from the American Chess Bulletin, December 1917.

White to mate in one move.

	Select Click for Answer
Okay, this was a trick question, which admittedly is not very Christmassy. It must be Black’s move; if it were White’s then there’s no legal move that Black can just have made. But on any Black move, White can now mate immediately: 1. … Kxb7 2. c8=Q# 1. … Bxb7 2. Na7# 1. … Rxc7 2. R(1)xc7# 1. … Rd8+ 2. cxd8=N# On anything else, White plays 2. Rb8#.

October 4, 2009January 22, 2013 | Puzzles

Retail Trouble

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.

October 3, 2009 | Puzzles

The Corpse Groom

A man once married his widow’s sister.

How is this possible?

	Select Click for Answer
The man married one woman, who died. He married her sister and then himself died, making a widow of the second wife. Thus he once married his widow’s sister.