Red White and Blue

I place four balls in a hat: a blue one, a white one, and two red ones. Now I draw two balls, look at them, and announce that at least one of them is red. What is the chance that the other is red?

	Select Click for Answer
It’s 1 in 5. Six possible pairings can be drawn from the hat: red 1 / red 2 red 1 / white red 2 / white red 1 / blue red 2 / blue white / blue We know that the last has not been drawn. That leaves 5 possible combinations, so the possibility of red 1 / red 2 is 1 in 5. “Many people cannot accept that the solution is not 1 in 3,” writes Erwin Brecher, “and of course it would be, if the balls had been drawn out separately and the color of the first ball announced as red before the second had been drawn out. However, as both balls had been drawn together, and then the color of one of the balls announced, then the above solution, 1 in 5, must be the correct one.”

Click for Answer

May 13, 2012February 4, 2013 | Puzzles

Black and White

dehler chess problem

By O. Dehler, Tidskrift för Schack, 1928. White to mate in two moves.

	Select Click for Answer
1. Qh7 (K moves) 2. e8=Q#.

May 11, 2012February 4, 2013 | Puzzles

Sand Reckoning

Using only a 4-minute hourglass and a 7-minute hourglass, how can you measure 9 minutes?

	Select Click for Answer
Turn over both hourglasses. When the 4-minute glass has run out, turn it over. When the 7-minute glass finishes, turn it over and let it run until the 4-minute glass has run out. At this point we’re at the 8-minute mark and the lower bulb of the 7-minute glass contains 1 minute’s worth of sand. Turn it over to measure the final minute.

May 7, 2012February 4, 2013 | Puzzles

Spin Control

We’re playing Russian roulette. The revolver has six chambers, all empty. I put bullets in two adjacent chambers, spin the cylinder, hold the gun to my head, and pull the trigger. It clicks. Now it’s your turn. Before pulling the trigger, you can choose to spin the cylinder again or leave it as it is. Which is better?

	Select Click for Answer
It’s better not to spin it. Two of the six chambers are loaded, so my chance of surviving was 4/6. But you know that the hammer fell on an empty chamber. Of the four empty chambers, only one is followed by a loaded one. So if you simply pull the trigger, you have a 3/4 chance of surviving. That’s better than 4/6, so you’re better off not spinning the cylinder.

May 6, 2012February 4, 2013 | Puzzles

Secret Entrance

Puzzle maven Noboyuki Yoshigahara noticed this sign on the glass door of an Osaka restaurant:

secret entrance puzzle

What is its meaning?

	Select Click for Answer
The words PULL and PUSH were painted on opposite sites of the door.

May 4, 2012February 4, 2013 | Puzzles

Black and White

t.r. dawson chess problem

By T.R. Dawson, Chess Amateur, 1920. White to mate in two moves.

	Select Click for Answer
1. b8=N! Kxe8 2. Qg8#

May 3, 2012March 1, 2013 | Puzzles

Making Way

A man is 4/7 across a train trestle when he sees a train coming. To get off the trestle, he can run toward the train or away from it. As it happens, in either case he’ll reach safety just as the locomotive passes him. If he runs at 20 kph, how fast is the train going?

	Select Click for Answer
If he runs toward the train, he’ll cover the remaining 3/7 of the trestle and meet the train at the far end. This means that if he runs away from the train, he’ll have covered 3/7 of the trestle (with 1/7 to go) when the train reaches the far end. He’ll then run the remaining 1/7 while the locomotive crosses all 7/7 and passes him. So the train is traveling at 7 times his speed, or 140 kph.

May 2, 2012February 1, 2013 | Puzzles

Strictly Speaking

Six logicians finish dinner. The waitress asks, “Do you all want coffee?”

First logician: “I don’t know.”

Second logician: “I don’t know.”

Third logician: “I don’t know.”

Fourth logician: “I don’t know.”

Fifth logician: “I don’t know.”

Sixth logician: “No.”

Who gets coffee and why?

	Select Click for Answer
The waitress has asked, “Do you all want coffee?” In saying “I don’t know,” each of the first five logicians is saying, “I want coffee, and at this moment it does appear possible that all six of us do, but we don’t yet have enough information to say so definitively.” The sixth logician doesn’t want coffee, so he’s able to say for certain that not everyone in the group does. So the waitress serves coffee to the first five logicians.

Click for Answer

May 1, 2012February 1, 2013 | Puzzles

Good Hands

A surgeon wears sterile gloves both to protect his patient and to protect himself. Can a hard-pressed surgeon with only two pairs of sterile gloves operate on three patients while keeping everyone safe?

	Select Click for Answer
Yes. He puts on both pairs of gloves and performs the first operation. He puts aside the outer pair of gloves and performs the second operation. Then he turns the first pair inside out and puts them on over the now-used second pair. This puts the two non-sterile sides in contact while keeping his hands in their sterile state and making the remaining sterile side (formerly the inside) of the first pair of gloves available for use in the third operation.

Click for Answer

April 30, 2012February 1, 2013 | Puzzles

War Games

Andy and Bob play rock-paper-scissors 10 times. Andy plays 3 rocks, 6 scissors, and 1 paper (in some order), and Bob plays 2 rocks, 4 scissors, and 4 paper. There are no ties. Who wins?

	Select Click for Answer
If there were no ties, then Andy’s 6 scissors used up all of Bob’s non-scissors plays (2 rocks and 4 paper). That means that Bob’s remaining plays, 4 scissors, were used against Andy’s 3 rocks and 1 paper: Andy won. (By Yoshinao Katagiri, via Nob Yoshigahara.)

April 29, 2012February 1, 2013 | Puzzles