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
Monthly Archives for May, 2013
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.
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
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
Given positive integers h,k and a real >0 show that there exists positive integers m and n so that
. -- via the whiteboard on 2nd floor of Packard.
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.
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"
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"
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
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 be the sequence of prime numbers and . Exercise: Show that . Now the twin prime conjecture states that . We … Continue reading the story "Twin prime conjecture."