What does below Rebus mean ?

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If a shopkeeper can only place the weights on one side of the common balance. For example, if he has weights 1 and 3 then he can measure 1, 3 and 4 only. Now the question is how many minimum weights and names of the weights you will need to measure all weights from 1 to 1000? This is a fairly simple problem and very easy to prove also.

I come in different shapes and sizes.
Parts of me are curved, other parts are straight.
You can put me anywhere you like,
but there is only one right place for me.
What am I?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

What does this mean?

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An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

I look at you, you look at me I raise my right, you raise your left. What am I?

John’s parents have three sons: Snap, Crackle, and what’s the name of the third son?

As a whole I am both
safe and secure.

Behead me and I become
a place of meeting.

Behead me again and I am
the partner of ready.

Restore me, and I become
the domain of beasts.

What am I?

A girl says this to her best friend: “I was born in 1955, and I celebrated my 17th birthday last weekend.” Her best friend thinks she’s lying, but she’s actually correct. How is that possible?