Before you read the rest, maybe you should have a look at Shawn’s blog… as what’s below may spoil the puzzle.
Every math week, I plan to provide a math challenge which could take you seconds to hours to solve, assuming you don’t cheat by using technology to solve it for you.
Today, I offer a time filler I occasionally use while substituting a junior or senior high math class that has “completed” all of its work, usually before I even enter class. I learned this problem from Blaine Dowler of Sylvan Learning. Usually I reward the first person who solves it, and usually it is the “weakest” student who does it.
The challenge is: If the product of two numbers is two and their sum is five, what is the simplest sum of their inverses?
I think I understand why the “weakest” student answers first, because the naive answer is the correct one:
Let our numbers be and . So:
We are looking to solve
Have to say this did not occur to me immediately at all, though I could hear a faint voice telling me to try it for some time before I actually did.