2006 AIME I Problems/Problem 2
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 | ||
All AIME Problems and Solutions |