2011 AMC 10B Problems/Problem 23
Revision as of 20:40, 25 February 2011 by Epicfailiure (talk | contribs) (Created page with '==Problem== What is the hundreds digit of 2011^2011? (A) 1 (B) 3 (C) 4 (D) 6 (E) 8 ==Solution== (2000 + 11) ^ 2011 mod 1000 11^2011 mod 1000 (10 + 1)^2011 mod 1000 2011C2 *…')
Problem
What is the hundreds digit of 2011^2011?
(A) 1 (B) 3 (C) 4 (D) 6 (E) 8
Solution
(2000 + 11) ^ 2011 mod 1000 11^2011 mod 1000 (10 + 1)^2011 mod 1000 2011C2 * 10^2 + 2011C1 * 10 + 1 mod 1000 500 + 110 + 1 mod 1000 611 mod 1000
So we know the last three digits of 2011 ^ 2011 is 611, and so the hundreds digit is 6 (D).
