Blindfold game

A blindfolded man is asked to sit in the front of a carrom board.
The holes of the board are shut with lids in random order, i.e. any
number of all the four holes can be shut or open. Now the man is
supposed to touch any two holes at a time and can do the following.
* Open the closed hole.
* Close the open hole.
* Let the hole be as it is.
After he has done it, the carrom board is rotated and again brought
to some position. The man is again not aware of what are the holes
which are open or closed.

How many minimum number of turns does the blindfolded man require
to either open all the holes or close all the holes?
Note that whenever all the holes are either open or close, there
will be an alarm so that the blindfolded man will know that he has won.

Birthday Probability Problem

What are the chances that at least two out of a group of fifty people
share the same birthday?

Find the sum of digits ?

Find sum of digits of D.
Let A= 1999¹⁹⁹⁹
B = sum of digits of A, C = sum of digits of B, D = sum of digits of C.

Cube puzzle

If you take a marker and start from a corner on a cube, what is the
maximum number of edges you can trace across if you never trace
across the same edge twice, never remove the marker from the cube,
and never trace anywhere on the cube, except for the corners & edges?

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?