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I have one too.
The numbers from 1 to 13 are sorted in a list like this {1,2,3,4,5,6,7,8,9,10,11,12,13}. A person comes over and picks a random number from 7 to 12 inclusive. He then cuts the list at that number like this
{1,2,3,4,5,6,7,8,9,10,11,12,13}
random number he picks is 9, so he cuts the list like this
{10,11,12,13} and {1,2,3,4,5,6,7,8,9} and merges the two lists into 1 list again.
{10,11,12,13,1,2,3,4,5,6,7,8,9}
It was so much fun he does it again:
{10,11,12,13,1,2,3,4,5,6,7,8,9}
random number = 7 he again breaks the list into
{4,5,6,7,8,9} and {10,11,12,13,1,2,3}
and again he merges this into 1 big list
{4,5,6,7,8,9,10,11,12,13,1,2,3}
he repeats this process again and again and then he gets a thought. What is the expected number of times he must do this for the list to come back to {1,2,3,4,5,6,7,8,9,10,11,12,13}?
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A person picks from the set of numbers {1,2,3,...100} eighty of them without replacement that sum to 3690. In how many ways can they do that?
Merry Christmas to everyone!
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