Strange killing

A girl, at the funeral of her mother, met a guy whom she did not know. She fell for him and just kept looking at him.Sometime later she realized that the guy is gone and she forgot to take the number of the guy and now she can't find him. A few days later she killed her elder brother.
Question: What is her motive in killing her brother ?

9. Robbery in a bank

The police rounded up Jim, Bud and Sam yesterday, because one of them was suspected of having robbed a bank. The three suspects made the following statements under intensive questioning: Jim: I’m innocent. Bud: I’m innocent. Sam: Bud is guilty. If only one of these statements is true, who robbed the bank?

8. Row, Row, Row Your Trees

How can seven trees be planted such that there are six rows of trees in straight lines consisting of three trees?

7. Brown Eyes and Red Eyes

There is an island of monks where everyone has either brown eyes or red eyes. Monks who have red eyes are cursed, and are supposed to commit suicide at midnight. However, no one ever talks about what color eyes they have, because the monks have a vow of silence. Thus, no one knows their own eye color; they can only see the eye colors of other people, and not mention them. Every day, the monks enjoy a silent brunch together at a round table. One day, a tourist visits the island monastery, and, unaware that he’s not supposed to talk about eyes, says “At least one of you has red eyes.” Having acquired this new information, something dramatic happens among the monks. What happens?

5. Globe Traversal

How many places are there on earth where one could walk one mile south, then one mile west, then one mile north and end up in the same spot? Assume the earth is a solid smooth sphere.

4. Glass Half Full

You are in an empty room with a transparent glass of water. The glass is a right cylinder and appears to be half full. How can you accurately figure out whether the glass is half full, more than half full, or less than half full? You have no rulers or writing utensils.

2. Cork, Bottle, Coin

You put a coin in an empty bottle and insert a cork in the bottle’s opening. How can you remove the coin without taking out the cork or breaking the bottle?

1. Burning Ropes

You are given two ropes and a lighter. Each of the two ropes has the following property: if you light one end of the rope, it will take exactly one hour to burn to the other end. It doesn’t necessarily burn at a uniform rate. How can you measure a period of 45 minutes?

Interesting and Funny riddles!!

Hey Here are some funny riddles you might want to solve and laugh at

#1.  Which is correct "The yolk of the egg is white" or "The egg yolk is white?"

#2.You bury me when I'm alive,
and dig me up only when I die.

#3.Sad, sick, or sloppy I'll help you out,
Use me right and I'll cover your snout.

What am I?
#4 Why don't mountains catch colds?

#5 What is the longest word in the dictionary?

Answers will be posted in the Answers section. 

YummY Pizza But tricky distribution

A  inch diameter round pizza has been sliced by  straight cuts, leaving a right triangle in the middle as shown here

The edge of the pizza has been cut into  arcs, one each of the following, in degrees, totaling  degrees

but not necessarily in that order. The maximum area, in square inches, this right triangle piece in the middle can have can be expressed as

where  are integers (which may be negative). Find

Integer  is positive. Do not rely on diagram to guess arcs in degrees.

WHAT!!!! you must be joking

Circle in a chess board

Consider an infinite chessboard, where the squares have side length of 1. The squares are colored black and white alternately. The (finite) radius of the largest circle whose circumference can be drawn completely on the white squares (hence you can see the entire circle) has the form , where  and  are integers,  and  are coprime, and  is not divisible by the square of any prime. What is the value of ?

Details and assumptions

 and  are all allowed to be 1. In particular, if you think the the largest radius is , then your answer to this should be .

Easy...NAAH!! yeah!!

365 can be written as a sum of 2 consecutive perfect squares and also 3 consecutive perfect squares:What is the next number with this property? Give the last 3 digits of the number.

The perfect squares cannot be zero.

Number theory

Find the sum of all positive integral  such that there exists a permutation  of the set  such that

is a rational number.  denotes the -th term of the permutation.