Find the Key

With the help clues provided in the image, can you find the 5 digit key?

Find the Key




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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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John is found dead in a bare field. Nobody killed John,
John did not commit suicide.

Inspector Jacob found a bag just a few meters away from John which could save his life. What was in the bag?

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Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
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John has eleven friends. He has a bowl containing eleven apples. Now He wants to divide the eleven apples among his friends, in such a way that an apple should remain in his bowl.
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I possess a head

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Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

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There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

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I never was there, I am always to be.
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A hen, a dog, and a cat are stolen. Three suspects are arrested named Robin, Steve, and Tim. The police are sure that all of them stole one of the animals but they don't know who stole which animal.

Sherlock Holmes is appointed to identify and is provided with the following statements from the investigation.

Robin - Tim stole the hen
Steve - Tim stole the dog
Tim - Both Robin and Steve are lying. I neither stole a hen nor a dog.

Sherlock is somehow able to deduce that the man who stole the cat is telling a lie and the man who stole the hen is telling truth.

Can you help him find out who stole which animal?

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There is a barrel with no lid and some wine in it. 'This barrel of wine is more than half full,' said Curly. 'No it's not,' says Mo. 'It's less than half full.' Without any measuring implements and without removing any wine from the barrel, how can they easily determine who is correct?

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