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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