2006 AIME I Problems/Problem 2

Problem

Let set $\mathcal{A}$ be a 90-element subset of $\{1,2,3,\ldots,100\},$ and let $S$ be the sum of the elements of $\mathcal{A}.$ Find the number of possible values of $S.$

Solution

The smallest S is $1+2+ \cdots +90=91\times45=4095$ . The largest S is $11+12+ \cdots +100=111\times45=4995$ . All numbers between 4095 and 4995 are possible values of S, so the number of possible values of S is $4995-4095+1=901$ .

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2006 AIME I Problems/Problem 2

Problem

Solution

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