## Town House Escape Game

Posted on: January 27th, 2013 by

Find clues to escape the apartment. Here  is the link.

## Frog Leap Game

Posted on: January 21st, 2013 by

The puzzle with the image can be accessed here. Start in this configuration with 7 rocks: green frog - green frog - green frog - empty rock - brown frog - brown frog - brown frog See how quickly you can switch the frogs to the opposite side of the pond. Green frogs can only hop to the right. Brown frogs can only hop to the left. Frogs Continue reading the story "Frog Leap Game"

## prof. montanaris quals question

Posted on: January 20th, 2013 by
1

You are given an N x N board. Each cell can have at most 4 neighbors (left, right, up, down).  You are allowed to "infect" k cells on the board. At each time step: 1. An "infected" cell remains "infected". 2. A "clean" cell becomes "infected" if atleast two of its neighbors are "infected". What is the minimum value of k and the initial infection pattern, so that eventually, the Continue reading the story "prof. montanaris quals question"

## Third Child's Name

Posted on: January 20th, 2013 by

1. Before Mt. Everest was discovered, what was the highest mountain in the world?
2. Johnny’s mother had three children. The first child was named April. The second child was named May. What was the third child’s name?
via Forbes.

## Random point in an equilateral triangle

Posted on: January 20th, 2013 by

A point P is chosen at random inside an equilateral triangle of side length 1.  Find the expected value of the sum of the (perpendicular) distances from P to the three sides of the triangle. via Nick's Mathematical Puzzles: 111 to 120.

## Powers of 2: deleted digit

Posted on: January 20th, 2013 by

Find all powers of 2 such that, after deleting the first digit, another power of 2 remains.  (For example, 25 = 32.  On deleting the initial 3, we are left with 2 = 21.)  Numbers are written in standard decimal notation, with no leading zeroes. via Nick's Mathematical Puzzles: 111 to 120.

## Factorial plus one

Posted on: January 20th, 2013 by

Let n be a positive integer.  Prove that n! + 1 is composite for infinitely many values of n. via Nick's Mathematical Puzzles: 111 to 120.

## Aces in Bridge Hands

Posted on: January 18th, 2013 by

Someone deals you a bridge hand 13 cards from a regular deck of 52 cards. You look at the hand and notice you have an Ace and say “I have an Ace”. What is the probability that you have another Ace?The cards are collected and different hand is dealt. This time you look at your hand and state “I have the Ace of Spades” which Continue reading the story "Aces in Bridge Hands"

## Elastic collisions and $\pi$

Posted on: January 17th, 2013 by
1

Here is a surprising relation between elastic collisions and $\pi$: Start with a large ball of mass $16*100^N$ kg. on the very left, a small ball of mass $1$ kg. to it's right and a wall to the very right. Send the large ball towards the small ball with an initial velocity $u_0$. The small ball will keep bouncing back and forth between the large ball Continue reading the story "Elastic collisions and $\pi$"

## IIT-Madras ready for mass production of artificial blood - The Times of India

Posted on: January 16th, 2013 by