In how many distinct ways can you tile a 2xn board using n pieces of 2x1 dominoes?

## Monthly Archives for January, 2014

## Inheritance

An Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower will win. The brothers, after wandering aimlessly for days,ask a wise man for advise. After hearing the advice they jump on the camels and race as fast as they can to the city. What does the wise …

**Continue reading the story**"Inheritance"## coin play

A large bag of coins is emptied on the floor such that no two coins overlap each other.
1. A child randomly selects a coin on the floor.
2. If the coin is heads, the child turns it over to show tails.
3. If the coin is tails, the child flips the coin in the air and likr before, doesn't overlap another.
4. …

**Continue reading the story**"coin play"## Hat puzzle

5 girls stand in a circle. Each girl wears a red hat or a blue hat. Each girl is blind-folded and is told the hat color of the two people adjacent to her on the circle. The five girls need to come up with a strategy to guess their hat colors simultaneously. Is it possible?
- via Australian Mathematical Society Gazette puzzle corner

## Average speed

Suppose a bicycle's average speed in any 10 minute interval is 18 miles per hour. How much distance will the bicycle travel in 25 minutes?
- via Australian Mathematical society Gazette puzzle corner

## Number operations

Suppose you are playing with fractions 1,1/2,1/3,.... 1/100. At each step, you take two of the fractions x,y and replace them by a function f(x,y). You keep repeating this process until only one number remains. What are all the possible values that the remaining number can take if f(a,b)=ab+a+b? Can you solve the puzzle again if f(a,b)=ab/(a+b)?
- via Australian mathematical society puzzle corner 34