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

A man escapes from jail using help from his girlfriend. The investigators suspect four girls of being the man's girlfriend.

Out of those four girls, one is his girlfriend who is lying. Two of the girls are completely innocent and are speaking the truth. One of the girls is the man's sister who is helping the girlfriend lie. Following are the statements from all four of them:

Ariana: "Myrna is his girlfriend."
Jane: "Angelina is lying."
Angelina: "Ariana is lying."
Myrna: "Jane is not his sister."

Can you find out who is the man's sister among them?

You have a square. What you have to do is cut and reassemble the square such that you create a Red Cross sign that has the same volume as that of the square.

What does this mathematical rebus means ?

You can see it everyday, But cannot touch it at will. What is it?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

Can you find the largest Three-digit number whose sum is 14 and whose square is less than 5,00,000?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

What does an Island and the letter T have in common?

Can you solve below mathematical equation?

2^1234 - 2^1233