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Monthly Archives for January, 2013
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"
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"
- Before Mt. Everest was discovered, what was the highest mountain in the world?
- 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?
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.
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.
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.
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"
Here is a surprising relation between elastic collisions and : Start with a large ball of mass kg. on the very left, a small ball of mass kg. to it's right and a wall to the very right. Send the large ball towards the small ball with an initial velocity . The small ball will keep bouncing back and forth between the large ball … Continue reading the story "Elastic collisions and "
IIT-Madras scientists have blood on their hands — and nobody is complaining. A team of scientists from the department of engineering design has been successful in creating enough red blood cells from stem cells to be used as 'artificial blood' in people who need transfusion. Having proved their oxygen-carrying capacity, the RBCs will now go into 'mass production' before starting human trials in three years, scientists … Continue reading the story "IIT-Madras ready for mass production of artificial blood - The Times of India"