Suppose that n is a positive integer such that in base 7, then n can be expressed as \(\overline{ABC}_7\), and in base 11 then n can be expressed as \(\overline{CBA}_{11}\). Find the largest possible value of n in base 10.

Guest Feb 24, 2021

#1**+1 **

Please show me what you can do for yourself.

I mean expand ABC base 7 so that it is in base10

and expand CBA base 11 so that it is in base 10

then put the 2 equal to one another.

I organised it to get B in terms of A and C

Then I used a small amount of trial and error to find the answer that worked.

You will also need to think about what possibilities are there.

What possible numbers can A be?

What possible numbers can B be?

What possible numbers can C be?

Will A be bigger or will C be bigger?

I have done this question and there are only 2 solutions. Obviously one is bigger than the other.

Melody Feb 24, 2021