What is the probability that N points randomly chosen on the boundary of a circle lie in the same semicircle? via Microsoft research
Monthly Archives for May, 2013
Find the missing angle using only elementary geometry: via Think zone
You have a cable of 1000 wires between two telephone exchanges A and B that are 10km apart. Unfortunately, the wires are not labeled, so you don't know how the endpoint of a wire at A corresponds to an endpoint at B. All you have is a battery and a light-bulb. Of course, you have tape and pen for labeling the wires. What's the minimum distance … Continue reading the story "Label the wires"
For a natural number k, let S(k) denote the sum of the digits of k in it's decimal representation. For example, if k=231, S(k)=2+3+1=6. Show that among 2 consecutive natural numbers n and n+1, atleast one of them can be written in the form k+S(k). via Utah Math Puzzles
You play the following game: The game host has a shuffled deck of 52 cards: 26 red and 26 black. He keeps revealing one card at a time until all 52 cards are revealed. At any time, you can interrupt the host and bet that the next card is red. You get one and only one chance to bet. You HAVE to bet at some … Continue reading the story "Card betting puzzle"
In a rainy season , one day 3 huge ladies walking under a normal sized umbrella. The umbrella is not huge enough to accommodate all 3 ladies yet not a single lady got wet. Why ? via Brain Teasers
Let A,B be 2 2x2 matrices with integer entries. Suppose the matrices A,A+B,A+2B,A+3B,A+4B are all invertible and their inverses are also integer matrices. Then show that A+5B is invertible and it's inverse is an integer matrix. via the white board on the 2nd floor of Packard building, Stanford.
Consider the following statements: 1. THREE is a prime. 2. FOUR is a square. 3. EIGHT is a cube. Put different digits to the letters to make the statements correct! Note: T,F,E should be non-zero.