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Monthly Archives for March, 2013

Matrix with integer sums

Posted on: March 11th, 2013 by

Suppose M is a matrix with real entries. Suppose that each of it's rows sum to an integer, and so does each column. Can you always find a matrix \tilde{M} with integer entries that has the same sum along each row and column as M? --Via Kartik Venkat.

Largest network of cities

Posted on: March 10th, 2013 by
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Suppose that there are n cities. Suppose that between any 2 cities, there exists a road with probability c/n. Thus each city is on an average connected to c other cities (for large n). This road network forms a random graph. A connected component of this city network is a set of cities such that one can travel from one city in the set to Continue reading the story "Largest network of cities"

Chicken crosses road

Posted on: March 9th, 2013 by
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Why did the chicken cross the road? Watch this viral video for answer:

Black and white socks

Posted on: March 8th, 2013 by

You have 12 black socks and 12 white socks mixed up in a drawer. You're up very early and it's too dark to tell them apart. What's the smallest number of socks you need to take out (blindly) to be sure of having a matching pair? via Brain Teasers

Special sequence

Posted on: March 8th, 2013 by
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What is special about the following sequence of numbers? 8 5 4 9 1 7 6 10 3 2 0 via Brain Teasers

Read More About this Post Here

Posted on: March 7th, 2013 by
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A farmer challenges an engineer, a physicist, and a mathematician to fence off the largest amount of area using the least amount of fence. The engineer made his fence in a circle and said it was the most efficient. The physicist made a long line and said that the length was infinite. Then he said that fencing half of the Earth was the best. The mathematician laughed at Continue reading the story "Read More About this Post Here"

Water in the Cup

Posted on: March 6th, 2013 by

A man in a restaurant asked a waiter for a juice glass, a dinner plate, water, a match, and a lemon wedge. The man poured enough water onto the plate to cover it. "If you can get the water on the plate into this glass without touching or moving this plate, I will give you $100," the man said. "You can use the match and lemon Continue reading the story "Water in the Cup"

How do you empty a bathtub?

Posted on: March 5th, 2013 by

During a visit to a mental asylum, a visitor asked the Director what the criteria is that defines if a patient should be institutionalized. "Well," said the Director, "we fill up a bathtub. Then we offer a teaspoon, a teacup, and a bucket to the patient and ask the patient to empty the bathtub." Okay, here's your test: 1. Would you use the spoon? 2. Would you use Continue reading the story "How do you empty a bathtub?"

Monty hall?

Posted on: March 4th, 2013 by

You are in a game show. The host shows you 3 doors, leading to 3 different rooms. Two of the rooms contain a goat and one contains a car. Obviously, your goal is to find the door containing the car. You randomly choose one of the doors. Then the host opens an other door to a room that contains a goat. Now he gives you Continue reading the story "Monty hall?"

Million dollar question

Posted on: March 3rd, 2013 by
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In a particular nation, the currency consists of notes of four diļ¬€erent values: $1, $10, $100, and $1000. Can one have exactly half a million notes with a total value of exactly one million dollars? via Australian Mathematical Society

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