Difference between revisions of "2012 AMC 8 Problems/Problem 12"
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What is the units digit of <math>13^{2012}</math>? | What is the units digit of <math>13^{2012}</math>? | ||
Revision as of 11:56, 9 December 2012
Problem
What is the units digit of 
?
Solution
The problem wants us to find the units digit of , therefore, we can eliminate the tens digit of 
, because the tens digit will not affect the final result. So our new expression is 
. Now we need to look for a pattern in the units digit.
We observe that there is a pattern for the units digit which recurs every four powers of three. Using this pattern, we find that the units digit of is
.
See Also
| 2012 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
