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/

While sleeping, head should face which direction ? Which direction you sleep? Do you know the consequences?

The direction your head faces while sleeping has a strong effect on your physical and mental well-being. Head placement refers to the direction the top of your head points when lying down.
Art of Sleeping

We are advised to avoid sleeping with our head to the north or west.


We all know that our planet has a magnetic pole stretched from north to south with the positive pole at the north and the negative pole at the south. Now, health scientists tell us that we too have a similar magnetic stretch with the positive pole at the head and the negative one at the feet.

It is common knowledge that like poles repel and unlike poles attract not only scientific but also in social spheres. When we lay our heads on the north side, the two positive sides repel each other and there is a struggle between the two.

Since the earth has a greater magnetic force, we are always the losers, and rise in the morning with headache or heaviness

Additional Details

But when we lay our heads in the southern direction, there is mutual attraction and we wake up fit, fresh and free, unless afflicted by some illness.

We also know that our planet revolves itself from west to east, and sun's magnetic field enters earth from east side. This magnetic force enters our head if we lie with head on the east and exits through feet, promoting cool heads and warm feet as per the laws of magnetism and electricity. When the head is laid towards the west, cool feet and hot head -- result -- an unpleasant start for morning.

Now we may realize why the ancient people said, that our intellect improves by east facing head or house, and life lengthens with the head facing south.

North brings disease and west dulls the brain. They gave us a few more healing hints for a healthy sleep. Never lie on one side for long. Keep changing.

Conclusion:

Head to East

Benefits: Auspicious. Always make sure you put your head in the East direction as much as possible.

Avoid daytime sleep. Let the night food be light and early. Drink milk with honey.

Avoid reading serious or sensual literature straining the nerves. Repeat a few mantras to relax your mind before you sleep.

Head to South
Benefits: Auspicious. The best position for sleeping is with the top of your head pointing to the south and feet pointing north.

Head to North or West
Results: Dangerous. Never sleep with the top of your head pointing to the north and feet pointing to the south. Brings terrible dreams and disturbed sleep. You will feel miserable. Irritability, frustration and emotional instability will develop. It sucks your positive vibrations while you sleep. You will lose 50% of your willpower and your soul power will not increase while you sleep. Your physical and mental health will suffer.