What is the formula of pie?
2 answers:
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Use the pigeonhole principle.
Consider choosing
This selection guarantees that no two elements have a difference of 12. For example, in the first subset with
, the largest difference is 12 - 1 = 11. Then in the next subset with 
, the smallest difference between the least element of this subset with the previous subset is 25 - 12 = 13.
The last subset is problematic, however, because the last two elements of that subset are 48 + 53 = 101 and 48 + 54 = 102. We require that all the integers are no greater than 100, and that they are distinct, which means there must be two numbers
that belong to the set 
, and this will force at least one integer that makes up a pair with difference 12.
Consider choosing
This selection guarantees that no two elements have a difference of 12. For example, in the first subset with
The last subset is problematic, however, because the last two elements of that subset are 48 + 53 = 101 and 48 + 54 = 102. We require that all the integers are no greater than 100, and that they are distinct, which means there must be two numbers