Of Sets and Sums

Probability Level 3

Consider the set {1,2,3,4,5,6,7,8,9,10} \lbrace{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\rbrace}.

For each of its subsets, let M M be the greatest number. Find the last three digits of the sum of all the M M 's.

Assume that 00 is the greatest number of the empty subset.

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