MathDB

8

Part of 2001 AIME Problems

Problems(2)

7-10 Doubles

Source:

12/6/2005
Call a positive integer NN a <spanclass=′latex−italic′>7−10double</span><span class='latex-italic'>7-10 double</span> if the digits of the base-7 representation of NN form a base-10 number that is twice N.N. For example, 51 is a 7-10 double because its base-7 representation is 102. What is the largest 7-10 double?
AMCAIME
A Certain Function

Source:

12/28/2006
A certain function ff has the properties that f(3x)=3f(x)f(3x)=3f(x) for all positive real values of xx, and that f(x)=1−∣x−2∣f(x)=1-\mid x-2 \mid for 1≤x≤31\leq x \leq 3. Find the smallest xx for which f(x)=f(2001)f(x)=f(2001).
functionanalytic geometrygraphing linesslopesymmetry