More useful when broken

What is more useful when it is broken?




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Consider all the numbers between 1 and 1 million. Among all these numbers, there is something very special about the number 8 and the number 2202. What is it?

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In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
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You have a roll of cloth 1km long. You have a machine which cuts this roll into pieces of 10-meter-long cloth.

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Jim and Sarah are in a long-distance relationship. Jim buys an engagement ring for Sarah and wants to mail it to her. Unfortunately, the only way to ensure the ring will be received is to place a lock on the package. Jim has locks and Sarah has locks, but neither has keys for each other’s locks. How can they make sure the ring isn’t stolen?

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A container contains 100 eggs. They can be either fresh or rotten. What is sure is the fact that there is at least one fresh egg in that container.

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