Posts filed under ‘.logic’

The Nine Coins Puzzle

Suppose you have nine identical coins that all look alike. You also know that all coins are identical in weight except for one, which is lighter than the others, the counterfeit. The difference is only perceptible by using a special balance, but only the coins themselves can be weighed, and it can only be used twice in total.

Can you find the counterfeit coin with only two weighings?


Balance puzzle
Weighing 9 Balls

September 19, 2010 at 3:04 pm Leave a comment

City of Truths

Imagine you are on planet Trulie with only two inhabitants, one that always tells the truth, and the other that always lies. You reach a fork in the road with a sign to the City of Truths. Unfortunately, the road sign is down. Fortunately, a Trulian appears from nowhere. What question do you ask him to find the way to the City of Truth?

Adaptation of Doctor Spacemath from:
Fractals, Googols, and Other Mathematical Tales by Theoni Pappas

September 17, 2010 at 11:23 pm Leave a comment

Fox, Goose and Bag of Beans

Once upon a time a farmer went to market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of a river and hired a boat. But in crossing the river by boat, the farmer could carry only himself and a single one of his purchases – the fox, the goose, or the bag of the beans.

If left alone, the fox would eat the goose, and the goose would eat the beans.

The farmer’s challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact.

How did he do it?


Wikipedia: Fox, goose and bag of beans puzzle

September 15, 2010 at 4:02 pm Leave a comment

Wolf, Goat, and Cabbage

The Moscow Puzzles: 359 Mathematical Recreations (Math & Logic Puzzles)
by Boris Kordemsky

This problem can be found in eighth-century writings:

A man has to take a wolf, a goat, and some cabbage across a river. His rowboat can only hold the man plus either the wolf, the goat, or the cabbage. If he takes the cabbage with him, the wolf will eat the goat. If he takes the wolf, the goat will eat the cabbage. Only when the man is present are the goat and the cabbage safe from their enemies. All the same the man carries wolf, goat, and cabbage across the river. How?

mathcats variant:
Crossing the River (with a Wolf, a Goat, and a Cabbage) :

Sailor Cat needs to bring a wolf, a goat, and a cabbage across the river.
The boat is tiny and can only carry one passenger at a time.
If he leaves the wolf and the goat alone together, the wolf will eat the goat.
If he leaves the goat and the cabbage alone together, the goat will eat the cabbage.
How can he bring all three safely across the river?

Erich Prisner: Wolf, goat, cabbage, … applet+setup
Lulu’s games: The wolf, the goat, and the cabbage
Cut the Knot: Goat, Cabbage and Wolf applet

One at a Time

September 15, 2010 at 2:17 pm Leave a comment

Fractals, Googols, and Other Mathematical Tales

by Theoni Pappas

Fractals, Googols, and Other Mathematical Tales by Theoni Pappas

September 13, 2010 at 3:15 pm Leave a comment

Seven Socks

There are 7 red socks and 7 white socks in a drawer. If you must reach in the drawer blindfolded, what is the least number of socks you must pull out of the drawer so that you get either two reds or two whites?

Fractals, Googols, and Other Mathematical Tales by Theoni Pappas

September 13, 2010 at 5:55 am Leave a comment

Sneak Preview

Would it be less expensive for you to take a friend to the movies three times, or three friends one time?

Fractals, Googols, and Other Mathematical Tales by Theoni Pappas

September 13, 2010 at 5:05 am Leave a comment

The Snail Puzzle

A snail is climbing up a slippery 30 inch wall. It climbs 5 inches a minute, but then slides back 4 inches. How many minutes will it take to reach the top of the wall?

Fractals, Googols, and Other Mathematical Tales by Theoni Pappas

September 13, 2010 at 4:20 am Leave a comment

Black Eyes and Blue Eyes

The problem, put very simply, is the following: I own five beautiful slave girls, recently purchased from a Mongol prince. Two of those young enchantress’s have black eyes; the other three, blue eyes. The two have a truthful answer to any question, whereas the three with black eyes always give a truthful answer, whereas the three with blue eyes are born liars and never answer with the truth. In a few moments the five of them will be brought here, all of their faces covered by a heavy veil, which will make it impossible for you to see their faces. You must discover, with no room for error, which of them have black eyes and which blue eyes. You may question three of the five slaves, one question to each one. From the three answers, you must solve the problem and explain the precise reasoning that led you to your answer. Your Questions should be quite simple ones, well within the compass of these slaves to answer.

From THE MAN WHO COUNTED by Malba Tahan
Chapter 33: EYE TO EYE
Download: .pdf

September 12, 2010 at 4:46 pm Leave a comment

The Lightest Pearl

A merchant of Benares, in India, had in his possession eight pearls identical in shape, size, and color. Of these eight pearls, seven were the same weight, while the eighth weighed slightly less than the others. How could the merchant discover which pearl was lighter, using a scale but making only two weighings and not using any weights?

From THE MAN WHO COUNTED by Malba Tahan
Download: .pdf

September 12, 2010 at 4:01 pm 1 comment

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