A number(xyz) in base 7 if expressed in base 9 becomes(zyx). What is the hexadecimal equivalent of (xyz)?

What's the easiest way to do this?

The answer is F8. Here are some hints about the method:

1) write out what the number xyz means in base 7 and what zyx means in base 9. The first one is 7·7·x + 7·y + z, for example.

2) set the two expressions equal, and collect the x , y and z terms.

3) you should be able to see that y must be divisible by 8, but the digits x, y, and z must all be between 0 and 6, since they are the digits of a base 7 number. What does this tell you about y?

4) now you should be able to get a relationship between x and z, and again since they are between 0 and 6, there is only one solution.

5) once you have x, y and z, you can check that xyz in base 7 is the same number as zyx in base 9, and you can calculate this number.

6) convert it to base 16.

Hope this helps!

--Stuart Anderson