Saturday, January 3, 2004

2004 #03 and 39

Every year, they manage to work the date into question.  Here's this year's:
Difficulty: Pretty Simple.

Difficulty: Relies on a bunch of work and a couple AHA! moments.  Tough.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 03, answer 39.


  1. I could be wrong, but I think the answer provided (10/3) is incorrect. If I factor everything out, I get:

    2^3 * 2^2001 + 2 * 2^2001
    2^2 * 2^2001 + 2^2001

    This simplifies to 10/5 or 2. The answer given is 10/3. Is the bottom supposed to be minus sign instead of addition?

    (Cheating, I verified my answer by plugging it into my calculator.)

  2. You are correct. I mistakenly left the denominator with a plus instead of the minus that the original had. It's easier to fix the answer than remake the question, so away with the error!