What is full of holes but still holds water?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

How many squares, of any size, can you find on this chessboard which do not contain a Rook?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

There is a wide field of corn. A goose finds its way into the field and starts running. Can you find out till which point the goose can run into the field?

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

What numbers should go on the bottom line?
3 6 9 15
8 2 10 12
11 8 19 27
19 10 29 39
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