## Hitori

Posted on: January 21st, 2014 by
Try a game of Hitori. The object of Hitori is to eliminate cells in the grid until there are no duplicates in any row or column. To eliminate a cell, it must be turned black by clicking on it. You must do this, however, without placing any black cells next to each other on a side (touching diagonally is ok) or by placing black cells Continue reading the story "Hitori"

## Racing in an escalator

Posted on: January 20th, 2014 by
You race your friend in an escalator. Normally, you can climb 2 steps in the time it takes your friend to climb one. Suppose you reach the top of the escalator in 30 steps and your friend reaches the top in 20 steps. How many steps are visible on the escalator? - via Mind your decisions

## A game

Posted on: January 19th, 2014 by
2

You and your friend play the following game. Each of you secretly pick an integer between 1 and N and write it on a card. The winner is the one who picked the larger number, unless the other person is exactly 1 below the larger number in which case the smaller number wins. In case of a tie, you repeat the game. What is the optimal Continue reading the story "A game"

## Chess king's tour continued

Posted on: January 18th, 2014 by
This is a continuation of yesterday's puzzle. Now, the chess king pays a penalty if he makes a horizontal or vertical move. Diagonal moves are free. Find a loop for the king that visits all the squares exactly once and returns to the starting cell so as to minimize the number of horizontal or vertical moves.

## Chess King's tour

Posted on: January 16th, 2014 by
A chess king wants to visit each square on an 8x8 chessboard exactly once and finally come back to the starting square thus completing the loop. Show how he can accomplish that.

## Generating random numbers from coin flips

Posted on: January 15th, 2014 by
You have a fair coin that you can toss as many times as you like. Show how you can generate a discrete random number X that takes value 1 with probability p1, value 2 with probability p2, .... value n with probability pn (p1+p2+...pn=1). If you have taken a class in Information theory and find the above puzzle too easy, here is a harder puzzle: Show Continue reading the story "Generating random numbers from coin flips"

## Find the Golden year

Posted on: January 14th, 2014 by
You are given a table of names of scientists and their birth and death year, sorted alphabetically by the names of scientists. Devise an efficient algorithm to find the year when the largest number of scientists lived. - via Algorithmic puzzles

## A geometry problem

Posted on: January 13th, 2014 by
4

Show that the distance $d$ between the circumcenter and incenter of a triangle satisfies $d^2=R(R-2r)$ where $R$ is the circumradius and $r$ is the inradius. - via Euler

## King's reach

Posted on: January 12th, 2014 by
1

A king moves on an infinite chessboard. How many different squares are reachable by the king in n moves? - via Algorithmic puzzles

## Sliding puzzle

Posted on: January 11th, 2014 by