Log In

Post Archives from the ‘Puzzles’ Category



Next term in sequence:

Posted on: February 23rd, 2013 by
2

What is the next term in the following sequence? O, T, T, F, F, S, S, E, ... For hint: View comments.

Two bulbs vs one bulb

Posted on: February 14th, 2013 by
Comments Disabled
Suppose the life-time of a light bulb of type A is an exponential RV with mean 1 month, and that of type B is exponential with mean 2 months. Is it better to have 2 bulbs of type A or 1 bulb of type B? Come up with the answer without doing the math.

Prisoners and hats

Posted on: February 14th, 2013 by
Comments Disabled
Suppose there are 100 prisoners in a room. There are 100 different colors, and all colors are known to all the prisoners. Each prisoner gets a hat of a certain color. As usual, each prisoner can see everyone's hat except his own. The prisoners are asked to guess their respective hat colors simultaneously (they write their guesses on a piece of paper; their guess cannot Continue reading the story "Prisoners and hats"

Number of clumps of cars in a highway

Posted on: February 6th, 2013 by
1

Imagine N cars, each of which travels at a different maximum speed. Initially, the cars are queued in random order at the starting point of a semi infinite, one lane highway. Each car drives at the minimum of its maximum speed and the speed at which the car in front of it is driving. The cars will form clumps. How many such clumps will we have in expectation? What is Continue reading the story "Number of clumps of cars in a highway"

Town House Escape Game

Posted on: January 27th, 2013 by
Comments Disabled
Find clues to escape the apartment. Here  is the link.

Frog Leap Game

Posted on: January 21st, 2013 by
Comments Disabled
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
Comments Disabled
  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
Comments Disabled
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
Comments Disabled
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.

{"result":"error", "message":"You can't access this resource as it requires an 'view' access for the website id = 1."}