MathDB

14

Part of 2017 AIME Problems

Problems(2)

My sound when AIME drowns me: logloglog

Source: 2017 AIME I #14

3/8/2017
Let a>1a > 1 and x>1x > 1 satisfy log⁡a(log⁡a(log⁡a2)+log⁡a24−128)=128\log_a(\log_a(\log_a 2) + \log_a 24 - 128) = 128 and log⁡a(log⁡ax)=256\log_a(\log_a x) = 256. Find the remainder when xx is divided by 10001000.
2017 AIME I
Crime and Punishmenten by ten by ten grid

Source: 2017 AIME II #14

3/23/2017
A 10×10×1010\times 10\times 10 grid of points consists of all points in space of the form (i,j,k)(i,j,k), where ii, jj, and kk are integers between 11 and 1010, inclusive. Find the number of different lines that contain exactly 88 of these points.
AMCAIMEAIME IICasework