Difference between revisions of "2003 AIME I Problems/Problem 3"
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== Solution == | == Solution == | ||
| + | Order the numbers in the set from greatest to least to reduce error: <math>\{34, 21, 13, 8, 5, 3, 2, 1\}.</math> | ||
Each [[element]] of the [[set]] will appear in <math>7</math> two-element [[subset]]s, once with each other number. | Each [[element]] of the [[set]] will appear in <math>7</math> two-element [[subset]]s, once with each other number. | ||
Revision as of 18:28, 18 February 2012
Problem
Let the set 
Susan makes a list as follows: for each two-element subset of 
she writes on her list the greater of the set's two elements. Find the sum of the numbers on the list.
Solution
Order the numbers in the set from greatest to least to reduce error: 
Each element of the set will appear in 
two-element subsets, once with each other number.
will be the greater number in 
subsets.
will be the greater number in 
subsets.
will be the greater number in 
subsets.
will be the greater number in 
subsets.- will be the greater number in
subsets. - will be the greater number in
subsets. - will be the greater number in
subsets. - will be the greater number in
subsets.
will be the greater number in 
will be the greater number in 
subsets.
will be the greater number in 
subsets.
will be the greater number in 
subsets.
subsets.
subsets.
subsets.
subsets.Therefore the desired sum is 
.
See also
| 2003 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
