2011 AMC 8 Problems/Problem 22
Revision as of 11:49, 12 November 2019 by Firebolt360 (talk | contribs)
Contents
Problem
What is the tens digit of ?
Solution 1
The first couple powers of are
As you can see, the last two digits cycle after every 4 powers.
From there, we go two more powers. The last two digits are
so the tens digit is
Solution 2
We want the tens digit
So, we take . That is congruent to
. From here, it is an easy bash, 7, 49, 43, 01, 07, 49, 43, 01, 07
See Also
2011 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.