2002 AMC 12B Problems/Problem 10
Contents
Problem
How many different integers can be expressed as the sum of three distinct members of the set ?
Solution 1
Subtracting 10 from each number in the set, and dividing the results by 3, we obtain the set . It is easy to see that we can get any integer between
and
inclusive as the sum of three elements from this set, for the total of
integers.
Solution 2
The set is an arithmetic sequence of numbers each more than a multiple of
. Thus the sum of any three numbers will be a multiple of
. All the multiples of
from
to
are possible, totaling to
integers.
oops
See also
2002 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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