1974 AHSME Problems/Problem 28
Problem
Which of the following is satisfied by all numbers of the form
where is or , is or ,..., is or ?
Solution
We can separate this into two cases.
Case 1: Here, clearly the minimum sum is when all of the are , so . The maximum sum is when the rest of the are all . In this case, Therefore, in this case, .
Case 2: Here, again, the minimum sum is when the rest of the are all , in which case the minimum sum is . The maximum sum is attained when all of the are . In that case, Therefore, in this case, .
Thus, we must have or , .
See Also
1974 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 27 |
Followed by Problem 29 | |
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