2006 AMC 10A Problems/Problem 20
Contents
[hide]Problem
Six distinct positive integers are randomly chosen between and , inclusive. What is the probability that some pair of these integers has a difference that is a multiple of ?
Solution
For two numbers to have a difference that is a multiple of , the numbers must be congruent (their remainders after division by must be the same).
are the possible values of numbers in . Since there are only possible values in and we are picking numbers, by the Pigeonhole Principle, two of the numbers must be congruent .
Therefore the probability that some pair of the integers has a difference that is a multiple of is .
Video Solution
~savannahsolver
See also
2006 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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All AMC 10 Problems and Solutions |
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