What is the next term in the following sequence? O, T, T, F, F, S, S, E, ... For hint: View comments.
Post Archives from the ‘Puzzles’ Category
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.
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"
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"
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.