G285 2021 MC-IME I

Problem 1

Let a recursive sequence $a_n$ be defined such that $a_1=20$ , and $a_n=16a_{n-1}+4$ . Find the last $3$ digits of $a_{100}$

Solution

Problem 2

If the number $abcd_{11}$ is a palindrome in base $7$ , and $dcba$ expressed in base $10$ does not begin with a nonzero digit, find the difference between the largest and smallest possible sum of $a+b+c+d$ .

Solution

Page

Toolbox

Search

G285 2021 MC-IME I

Problem 1

Problem 2