No calculators please, we are thinkers
Problem source: Strategies for solving problems in the BAMO contest (the Bay Area Mathematical Olympiad) by Tom Davis.
Problem source: Strategies for solving problems in the BAMO contest (the Bay Area Mathematical Olympiad) by Tom Davis.
March 4th, 2010 at 1:36 am
Let a=1000, b=990. Then this expression is
[(a+b)³-a³-b³]/[(a+b)ab]
=(3a²b+3ab²)/[(a+b)ab]
=3.
March 4th, 2010 at 8:23 pm
Agree, and I got the same result with a=1000, b=10; Richard has a much better eye for the elegant solution.
Of course, this suggests we could use ANY 3 numbers that were of the form a+b, a, b, and still end up with 3. Cute (another stupid math trick to amaze my friends with).