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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The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

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Should you stay, or switch, or doesn't it matter?

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Challenging

There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.