## Guess hat color

Posted on: March 14th, 2014 by
1

Consider the picture below:

In this picture, there are 4 prisoners buried in the ground. There is a brick wall separating A and B. C can see B and D can see both B and C. Between the 4 prisoners, 2 white and 2 black hats are worn. No one can see their own hat color. The hat color is fixed as shown in the picture. To survive, at least one prisoner must call out their hat color correctly. Who will call out the hat color?

- via Camworld

## Rational k-th power

Posted on: March 12th, 2014 by
1

For any k, the number A[k] is formed by writing all the perfect k-th powers in order after the decimal point. For example A[1]=0.1234567891011121314.... and A[2]=0.149162536496481100121144....
Is there a value of k for which A[k] is a rational number?

- via AMS math society

## Liars, truth-tellers, mathematicians and physicists

Posted on: March 10th, 2014 by
6

There are N mathematicians and N physicists in a circular table. Some of them are liars and some are truth-tellers. The number of truth tellers who are mathematicians is equal to the number of truth teller a who are physicists. They are all asked, "Is the person next to you a mathematician or a physicist?" They all reply "physicist." Show that N must be even.

- via AMS math society

## Guess a coin for freedom

Posted on: March 7th, 2014 by
5

A and B are prisoners. The jailer have them play a game. He places one coin on each cell of an 8x8 chessboard. Some are tails up and others are heads up. B cannot yet see the board. The jailer shows the board to A and selects a cell. He will allow A to flip exactly one coin on the board. Then B arrives. He is asked to inspect the board and then guess the cell selected by the jailer. If B guesses the correct cell among 64 options, A and B are set free. Otherwise, they are both executed. Is there a winning strategy for A and B? (They can co-operate and discuss a strategy before the game starts).

- via Algorithmic puzzles

## Five in Seven

Posted on: March 5th, 2014 by
Comments Disabled

You have 5 items of different weights and a two-pan balance scale with no weights. How can you sort the items in ascending order in just seven weighings?

- via Algorithmic puzzles

## Two dimensional sort

Posted on: March 3rd, 2014 by
Comments Disabled

You start with a shuffled deck of 52 cards numbered 1,2,3,...52. You place them in 4 rows and 13 columns. Then you sort each row in ascending order as per their number. Then you sort each column in ascending order. After this procedure, determine the maximum number of swaps needed to sort a particular row.

- via Algorithmic puzzles

## Squaring a triangle

Posted on: March 1st, 2014 by
5

A triangle is formed by arranging 1+3+5+7+...(2n-1) = n^2 coins as shown in the figure below.

What is the minimum number of coins that you need to move so that you can form a square that uses all the coins?

- via Algorithmic puzzles

## Diff sort

Posted on: February 27th, 2014 by
1

You are given an array of n real numbers. Arrange them so that the average difference between adjacent numbers is minimized. In other words, minimize ${1\over n-1}\sum_{i=1}^{n-1} |X[i]-X[j]|$.

- via Algorithmic puzzles

## Find the missing number

Posted on: February 25th, 2014 by
Comments Disabled

You have an array with 99 distinct entries, each entry being an integer from 1 to 100. Find the missing number in the shortest possible time and O(1) memory.

Bonus: Now you have an array with 98 distinct entries, each entry being an integer from 1 to 100. Find the two missing entries in the shortest possible time and O(1) memory.

- via Mind your decision

## Dividing a Pizza

Posted on: February 24th, 2014 by
2

Consider the circle shown below:

The diameter BM is divided in to 11 equal length segments: BC,CD,DE,...LM. Then we complete semicircles with diameters CM,DM,...KM,LM on the top of BM and semicircles with diameters BC,BD,BE,....BL on the bottom of BM. These semicircles divide the circle in to 11 blade-shaped objects. Show that all blades have the same area!

- via Quora

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