Punctuate

Posted on: May 31st, 2013 by

Counterintuitive probability

Posted on: May 31st, 2013 by
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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

From the picture below, can you tell whether the bus is travelling to the left or to the right? Preschoolers can get this puzzle. Can you? via Thomas Cover and via this link

Weight of watermelon

Posted on: May 29th, 2013 by
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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

Given positive integers h,k and a real $\epsilon$>0 show that there exists positive integers m and n so that

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

A Prime numbers puzzle

Posted on: May 27th, 2013 by
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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

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
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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
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."