Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

John speaks the truth only once a day in a week. Below are a few hints for you:

First: Days are Sunday, Monday and so on.
Second: One day he says, "I lie on Monday and Tuesday".
Third: On the next day, he says, "Today is either Thursday, Saturday or Sunday".
Fourth: On the next day, he says, "I lie on Wednesday and Friday".

Can you identify the day on which he speaks the truth?

How can you throw a ball as hard as you can and have it come back to you even if it doesn't hit anything there is nothing attached to it and no one else catches or throws it.

Can you find a five letter word that is left with only two letters if one is removed?

Solve the alphametic puzzle by replacing the alphabet with the number.

S T O R M +
S O L E S
=========
T O W E L
=========

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

Given that

(78)^9 = 6
And (69)^4 = 11

Can you find out

(99)^2 =?

(Note: This is Logical, not Mathematical)

A train leaves from point A for point B at 80 mph. After half an hour, another train leaves from point B for point A at 60 mph.

Which of the trains will be farther from point A when they meet ?

A few friends are enjoying their sea voyage in a boat full of apples. On the way, they felt hungry and thus decided to eat the apples. Together, they ate two dozen of apples. When they have eaten the apples, will there be any change in the water level?

Until it is measured, not known. Yet how you miss it when it has gone. What is it?