Guess My B'day

Source: Tanya Khovanova Blog

My birthday is in January. What is the smallest number of yes/no questions you need to ask to determine the day of my birthday.

Some Interesting Mathematics blogs

I keep on hunting the internet for good mathematical puzzles and discussions , sometimes I stumble upon very unknown and good to know mathmatical facts.

http://blog.tanyakhovanova.com/
http://gurmeet.net/puzzles/
http://pratikpoddarcse.blogspot.com/
http://mathematicsbloggers.blogspot.com/

Fixed point theorem

Source: Nash Equilibrium's derivative also, in Martin's Gardener My best Mathematical and Logical Puzzles


Problem:  One morning at 6 am, a monk began climbing a tall mountain, which happened to only have one path to the top. He ascended the path at his leisure, taking some stops along the way. He reached the top at 8 pm.

The next morning at 6 am, the monk descended the mountain along the same path. He took several breaks along the way, and reached the bottom at 8 pm.

The amazing result: there is some spot on the path that the monk occupied at precisely the same time of day for both trips. Why is this?

This is true even if the monk took breaks to meditate, chatted it up with a fellow traveler, or if he took some time to massage his feet. You get the point: it really does not matter what he did during the trips going up or down.

Beauty Contest

Source: Some Basic Game theory books


Problem: 


Pick a number from 0 to 100. The winner is the person who chooses the number closest to 2/3rds of the group's average response. 
What is the rational answer?

Soccer fan's dream

Source: Moscow Puzzles

Problem:
A soccer fan upset by the defeat of his favorite team slept restlessly. In his dream ,he saw the goalkeeper was practicing alone in a large room, tossing the ball against a wall and catching it.
But the goalkeeper got smaller and smaller and changed into a ping pong ball, and the soccer ball swelled into a huge cast iron ball.
The iron ball circled around madly, trying to crush the ping pong ball which darted desperately about .
Could the ping pong ball find safety without leaving the floor?

The Traveler

Source: Martin Gardener's -My Best Mathematical And Logical Puzzles

Problem: A traveler comes to a fork in the road which leads to two villages. In one village the people always tell lies and in the other village the people always tell the truth. The traveler needs to conduct business in the village where everyone always tells the truth. A man from one of the villages is standing in the middle of the fork, so there is no indication of which village he comes from. The traveler approaches the man and asks him just one question. From the man’s answer, he knows which road to follow. What is the question?

Solution : - in comments below

Birthday problem or a paradox

Source: wikipedia

Problem: There is a big line of people waiting outside a theater for buying tickets. The theater owner comes out and announces that the first person to have a birthday same as someone standing before him in the line gets a free ticket. Where will you stand to maximize your chance.