2006 AIME I Problems/Problem 2
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Problem
Let set be a 90-element subset of and let be the sum of the elements of Find the number of possible values of
Solution
The smallest is . The largest is . All numbers between and are possible values of S, so the number of possible values of S is .
Alternatively, for ease of calculation, let set be a 10-element subset of T\mathcal{B}ST=5050-ST1+2+ \ldots +10 = 5591+92+ \ldots + 100 = 955955-55+1=\boxed{901}.
See also
2006 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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