Three Digit Number

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?




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A man desired to get into his work building, however he had forgotten his code.
However, he did recollect five pieces of information
* Fifth number + Third number = 14
* The fourth number is one more than the second number.
* The first number is one less than twice the second number.
* The second number and the third number equals 10.
* The sum of all five numbers is 30.

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