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Monthly Archives for May, 2013


Posted on: May 31st, 2013 by
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Make the sentence below grammatically correct by adding punctuation. Alex while Emily had had had had had had had had had had had a better effect on the teacher via curiouser.co.uk

Counterintuitive probability

Posted on: May 31st, 2013 by

1) Jack has 2 kids. One of them is a girl. What is the probability that the other kid is also a girl? 2) Jack has 2 kids. At least one of them is a girl. What is the probability that both the kids are girls? via EE quals questions.

Which way is the bus travelling?

Posted on: May 30th, 2013 by
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From the picture below, can you tell whether the bus is travelling to the left or to the right? Picture of a bus Preschoolers can get this puzzle. Can you? via Thomas Cover and via this link

Weight of watermelon

Posted on: May 29th, 2013 by

A counter-intuitive puzzle: A watermelon weighs 1kg. It contains 99% water. You let some water in the watermelon evaporate until the watermelon contains 98% water. What is the weight of the watermelon after the evaporation? Try to guess the answer before solving for it. via Counter-intuitive Conundrums

Rational approximations

Posted on: May 28th, 2013 by
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Given positive integers h,k and a real \epsilon>0 show that there exists positive integers m and n so that

\epsilon < |h\sqrt{m}-k\sqrt{n}| < 2\epsilon

. -- via the whiteboard on 2nd floor of Packard.

A Prime numbers puzzle

Posted on: May 27th, 2013 by

Let p(n) denote the number of primes less than n. Show that there are infinitely many n for which n is divisible by p(n). via the white board on 2nd floor of Packard.

Probability and maximum entropy

Posted on: May 26th, 2013 by
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Information theorists may already be familiar with this, but it's an interesting puzzle for non-information-theorists. Here are two questions: First an easy one: Suppose you roll a coin 1000 times. What is the conditional probability that the first roll is heads given that you observe 700 heads out of the 1000 rolls? Next a hard one: Suppose you roll a die (faces numbered 1 through 6) 1000 Continue reading the story "Probability and maximum entropy"

How to hunt a zombie

Posted on: May 25th, 2013 by

A zombie moves along a 1 dimensional line. It starts at position x, and at each time step, it moves y steps to the right. x and y are integers unknown to you. (If y is negative, it means the zombie moves -y steps to the left.) After each time step, you are allowed to examine any integer position and ask if the zombie is Continue reading the story "How to hunt a zombie"

Find the range

Posted on: May 24th, 2013 by
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Suppose the sum of 5 positive real numbers is 7 and the sum of their squares is 10. Show that each number should lie between 1 and 9/5. via Nick's mathematical puzzles

Twin prime conjecture.

Posted on: May 24th, 2013 by

Recently, a chinese mathematician made progress towards the twin prime conjecture. For an informal introduction, read it in the news here. I cannot resist being formal, so let me give a puzzle and explain the conjecture as well: Let p_n be the sequence of prime numbers and q_n=p_{n+1}-p_n. Exercise: Show that \limsup_{n\rightarrow \infty} q_n = \infty. Now the twin prime conjecture states that \liminf_{n\rightarrow \infty} q_n = 2. We Continue reading the story "Twin prime conjecture."

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