Difference between revisions of "2006 AIME I Problems/Problem 2"
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== Solution == | == Solution == | ||
− | + | The smallest S is <math>1+2+...+90=91\times45=4095</math>. The largest S is <math>11+12+...+100=111\times45=4995</math>. All numbers between 4095 and 4995 are possible values of S, so the number of possible values of S is <math>4995-4095+1=901</math>. | |
== See also == | == See also == | ||
* [[2006 AIME I Problems]] | * [[2006 AIME I Problems]] |
Revision as of 00:23, 1 July 2006
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 S is . The largest S is
. All numbers between 4095 and 4995 are possible values of S, so the number of possible values of S is
.