Difference between revisions of "2008 AIME I Problems/Problem 7"
(solution by samath) |
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Revision as of 13:45, 23 March 2008
Problem
Let be the set of all integers
such that
. For example,
is the set
. How many of the sets
do not contain a perfect square?
Solution
The difference between consecutive squares is
which means that all squares above
are more than 100 apart.
Then the first 25 sets (
) each have one perfect square. Also, since
, there are
other sets after
that have a square. Then there are
without a perfect square.
See also
2008 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |