Sum of Squares

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




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Queen Elizabeth organised a royal party.

To Avoid uninvited guest royal family set a password.
Jack (an uninvited person) plan to enter the party. He stand nearby the door.

First guest comes, the security person said 'twelve' and guest replied with six.
Second guest comes , the security person said 'six' and guest replied with 'three'.

Jack thought is enough and he walked to the entry point. The security person said 'eight' , Jack replied smilingly 'four'.
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A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
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There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
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How can one talk without saying a single word?

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In the picture that is attached with this question, you can find a square which comprises of four little squares inside it. Consider this square to be made with matchsticks. You have to remove two matchsticks such that only two squares remain instead of five.How will you do it ?

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Rearrange the letters in "new door" to make one word.

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You are in a room that has three switches and a closed door. The switches control three light bulbs on the other side of the door. Once you open the door, you may never touch the switches again. How can you definitively tell which switch is connected to each of the light bulbs?

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Rubik’s Cube

The inventor of the Rubik’s Cube didn’t realize he’d built a puzzle until he scrambled it the first time and tried to restore it.