2002 AMC 12A Problems/Problem 17: Difference between revisions
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== Problem == | == Problem == | ||
<!-- don't remove the following tag, for PoTW on the Wiki front page--><onlyinclude>Several sets of prime numbers, such as < | <!-- don't remove the following tag, for PoTW on the Wiki front page--><onlyinclude>Several sets of prime numbers, such as <imath>\{7,83,421,659\}</imath> use each of the nine nonzero digits exactly once. What is the smallest possible sum such a set of primes could have?<!-- don't remove the following tag, for PoTW on the Wiki front page--></onlyinclude> | ||
< | <imath> | ||
\text{(A) }193 | \text{(A) }193 | ||
\qquad | \qquad | ||
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\qquad | \qquad | ||
\text{(E) }447 | \text{(E) }447 | ||
</ | </imath> | ||
== Solution == | == Solution == | ||
Latest revision as of 16:00, 9 November 2025
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 sets work: 
or 
.
Thus the answer is 
.
Video Solution
https://www.youtube.com/watch?v=V6z7GiitBUM
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 | |
These problems are copyrighted © by the Mathematical Association of America. 
