2002 AMC 12A Problems/Problem 17: Difference between revisions
New page: == Problem == Several sets of prime numbers, such as <math>\{7,83,421,659\}</math> use each of the nine nonzero digits exactly once. What is the smallest possible sum such a set of primes... |
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We can indeed create a set of primes with this sum, for example the following set works: <math>\{ 41, 67, 89, 2, 3, 5 \}</math>. | We can indeed create a set of primes with this sum, for example the following set works: <math>\{ 41, 67, 89, 2, 3, 5 \}</math>. | ||
Thus the answer is <math>\boxed{207}</math>. | Thus the answer is <math>\boxed{(B)207}</math>. | ||
== See Also == | == See Also == | ||
{{AMC12 box|year=2002|ab=A|num-b=16|num-a=18}} | {{AMC12 box|year=2002|ab=A|num-b=16|num-a=18}} | ||
Revision as of 23:13, 1 July 2013
Problem
Several sets of prime numbers, such as 
use each of the nine nonzero digits exactly once. What is the smallest possible sum such a set of primes could have?
Solution
Neither of the digits 
, 
, and 
can be a units digit of a prime. Therefore the sum of the set is at least 
.
We can indeed create a set of primes with this sum, for example the following set works: 
.
Thus the answer is 
.
See Also
| 2002 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 16 |
Followed by Problem 18 |
| 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 | |
