Find the probability

In a hotel, rooms are numbered from 101 to 550. A room is chosen
at random. What is the probability that room number starts with
1, 2 or 3 and ends with 4, 5 or 6?

Find the ages of the chidren ?

Many years from now, two classmates met in a street.

The following is part of their discussion.

Student 1: Yes, I'm married and have three wounderful children.
Student 2: That's great! How old are they?
Student 1: Well, the product of their ages is 36.
Student 2: Hmm. That doesn't tell me enough. Give me another clue.
Student 1: OK. the sum of their ages is the number on that building
across the street.
Student 2: (After a few minutes of thinking with the aid of pencil and paper)
Ah ha! I've almost got it but I still need another clue.
Student 1: Very well. The oldest one has red hair.
Student 2: I've got it!

What were the ages of the children of student 1?

Last words of the soldier...

A soldier has been captured by the enemy and is sentenced to die.
His captors say: "You may make a statement. If you tell a lie, you will
be shot. If you tell the truth, you will be hanged."
He makes a statement and goes free. What could he have said?

Complete the sequence

1, 13, 2, 1, 5, 3, 2, 1, 4, 4, 7, 3, 1, 5, 3, 5, ___, ___

Eight queens problem

Place 8 queens in 8X8 chessboard such that none of them able to
capture any other by standard moves of queen. That is no 2 queens
would be able to attack each other.
[also try general queens problem of placing n queens in nxn chessboard]

Find the length of the bridge ?

There is a river which is 4100 inches wide, and the bridge across the
river is in such a way that one seventh of the overall length of the
bridge was on one side of the river and one eighth of the bridge was
on the other side of the river.
Find the total length of the bridge?

[Note: The bridge perfectly straight]

Chess board problem

what is maximum no. of kings which can be placed on a chessboard so
that no 2 of them put each other in check?
[provided all kings are of one color and check rule is applicable to
same color kings]