Online Course Discussion Forum
Week 1 HW AMC 12 Prep Course
Hi, I'm currently stuck on problem 9 on our homework, ie
Bernardo chooses a three-digit positive integer and writes both its base-5 and base-6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base-10 integers, he adds them to obtain an integer . For example, if , Bernardo writes the numbers and , and LeRoy obtains the sum . For how many choices of are the two rightmost digits of , in order, the same as those of ?
So far, I've found that N <= 4 mod 30 by looking at the ones digit for N in base 6, 5, and 10, and solving some congruences.
However, I have no idea where to go from here or how to find out what the possible tens digits of N in base 6 or N in base 5 could be.
I would really appreciate some help!
I see, thanks for the help! Just making sure, we multiply by 5 because of the 5 cases where N is congruent to 0, 1, 2, 3, and 4 mod 30 right?