## Medium puzzles

The stick drops and breaks at a random point distributed uniformly across the length. What is the expected length of the smaller part?

Solution
Source: Quant Interview
Enable Like and Comment

100 prisoners are lined up and assigned a random hat These hats are available in 10 different unique and distinguishable colors. Each prisoner can see the hats in front of him but not behind. Starting with the prisoner in the back of the line and moving forward, they must each, in turn, say only one word which must be the color like "red" or "blue" or "green" etc. If the word matches their hat color they are released, if not, they are killed on the spot. They can hear each others answers, no matter how far they are on the line. What strategy should be used to help release maximum number of prisoners?

Hint
Solution

N people team up and decide on a strategy for playing this game. Then they walk into a room. On entry to the room, each person is given a hat on which one of the first N natural numbers is written. There may be duplicate hat numbers. For example, for N=3, the 3 team members may get hats labeled 2, 0, 2. Each person can see the numbers written on the others' hats, but does not know the number written on his own hat. Every person then simultaneously guesses the number of his own hat. What strategy can the team follow to make sure that at least one person on the team guesses his hat number correctly?

Hint
Solution

I guessed 3 natural numbers - x,y,z. You can ask me 2 sums of these numbers with any integer coefficients - (a,b,c). That is, you give me a, b and c and I tell you the result of the expression a*x+b*y+c*z. Seeing the answer, you then give me the 2nd triplet of (a,b,c) & I will tell a*x+b*y+c*z. Give me the algorithm to find x,y and z.

Hint
Solution
Source: Quantnet Forums
Enable Like and Comment

An 8x8 chessboard can be entirely covered by 32 dominoes of size 2x1. Suppose we cut off two opposite corners of chess (i.e. two white blocks or two black blocks). Prove that now it is impossible to cover the remaining chessboard with 31 dominoes.

Hint
Solution
Source: Martin Gardner
Enable Like and Comment

Latest solved Puzzles

Difficulty Level