2002 AMC 10P Problems/Problem 15
Contents
Problem
What is the smallest integer for which any subset of
of size
must contain two numbers that differ by 8?
Solution
There are twelve pairs ,
,
,
,
in
that differ by 8. If we take
, it could be that we selected one element from each pair for the subset: the condition may not be fulfilled. By the Pigeonhole principle, in order to select at least one pair, it is necessary to select
elements.
~green_lotus
Solution 2
Use casework to find that the answer is D.
See Also
2002 AMC 10P (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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All AMC 10 Problems and Solutions |
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