Find the Probability.

Ravi is practicing throws for cricket. In his first four throws, he hits the stumps three times (success - 3, failure -1). It is given that, in his subsequent throws, the probability of hitting the stumps is equal to his success rate at that time (because of the confidence :) ).
For example, the probability of hitting the stumps in the 5th throw is 3/4. and if he succeeded in the 5th throw, the probability of hitting the stumps in the 6th throw would be 4/5.

So, what is the probability that, out of 100 throws, he succeeds in exactly 50 throws(including the first four throws)?

Two Geniuses...

Two geniuses are each assigned a positive integer and are told that the two numbers
differ by 1. They then take turns to ask each other, ‘Do you know my number
now?’. If the geniuses always respond to questions truthfully, prove that one of
them will eventually answer affirmatively.

Source(s): http://www.austms.org.au/

What is that number?

You have a number that consists of 6 different digits. This number multiplied by 2, 3, 4, 5, and 6 yields, in all cases, a new 6-digit number, which, in all cases, is a permutation of the original 6 different digits. What's the number?

source(s): http://thomer.com

Stretchy string

A rubber string is 10 meters long. There is a worm crawling from one end toward

the other at a speed of 1 metre per hour. Upon the passing of each hour, the

rubber string is stretched uniformly to become 1 metre longer than it just was.

Will the worm ever reach the other end of the string? How much time will it take to reach the other end (if the worm can reach the other end)?

Source(s): http://www.austms.org.au/

Some good Maths books

http://www.comms.engg.susx.ac.uk/fft/math/