Futility Closet

Solutions to Misc:

1. The first. A pound of gold is worth more than half a pound.
2. $2.
3. 6009.

1. Which is worth more, a pound of $10 gold pieces or half a pound of $20 gold pieces?
2. A kazoo costs $1 plus half its price. How much does it cost?
3. 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?

(Answers)

Solution to The Stopped Clock:

Before she leaves the house, Andrea winds her own clock and sets it to an arbitary 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.

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?

(Solution)

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.

Solution to Find the Theme, Part 2:

All are composed of U.S. state postal abbreviations.

What do these words have in common?

• CANDID
• MEMORIAL
• ALKYLAMINE

I’ll give the answer tomorrow.

Solution to Hell’s Bells:

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#.

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

White to mate in one move.

(Solution)

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.