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 , and let be the sum of the elements of . Note that the number of possible is the number of possible . The smallest possible is and the largest is , so the number of possible values of T, and therefore S, is .
See also
2006 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
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