Difference between revisions of "2016 AMC 10B Problems/Problem 8"
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+ | == Video Solution == | ||
+ | https://youtu.be/zfChnbMGLVQ?t=2683 | ||
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+ | ~ pi_is_3.14 | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2016|ab=B|num-b=7|num-a=9}} | {{AMC10 box|year=2016|ab=B|num-b=7|num-a=9}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 02:18, 17 January 2021
Problem
What is the tens digit of
Solution 1
Notice that, for , is congruent to when is even and when is odd. (Check for yourself). Since is even, and .
So the answer is .
Solution 2
In a very similar fashion, we find that , which equals . Next, since every power (greater than ) of every number ending in will end in (which can easily be verified), we get . (In this way, we don't have to worry about the exponent very much.) Finally, , and thus , as above.
Video Solution
~savannahsolver
Video Solution
https://youtu.be/zfChnbMGLVQ?t=2683
~ pi_is_3.14
See Also
2016 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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 10 Problems and Solutions |
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