One Way To Break A Tie

By Mike O’Hern, Center Director of Mathnasium of West Knoxville

Last month at our math learning center we hosted the 5th Annual TriMathalon.  What an absolute ball we had.  It’s a math competition, but it’s also just a big, fun event for second through fifth grade kids and their families.  We had games, prizes, and, of course, pizza (I’m not sure one could call a gathering an “event” without pizza).  Like the name implies, the competition is broken into three separate events – The Counting Game, Magic Squares, and Mental Math.

Now it was the fifth annual, but it was first time we hosted the event here in Knoxville.  The TriMathalon is held at many, many Mathnasium locations around the country on a single weekend, and each location has its local winners.  Then the results for each student are sent to the Mathnasium Headquarters in Los Angeles where they find the winners nationally.

Here’s the problem, though.  What if 50 different students get a perfect score on their work?  You would need a tie-breaker, right?  But how do you find a way to separate the most exceptional mathematicians in the group?

On your average math test there are a series of problems for which each has a specific and single correct answer.  “Count by 1/2’s starting at 1,” for example, must be answered with 1, 1 1/2, 2, 2 1/2, 3, 3 1/2, etc.  And we’ve already established that there are 50 kids around the country who will get all the answers correct if given another of these tests.

So the great thinkers at Mathnasium had the idea of having a tie-breaker that would test the creativity of each mathematician by giving a problem that was not limited to a single correct answer, but instead an infinite number of answers so that the best answer would be the winner – brilliant!

And now that the tie-breaker is complete and the winners have been announced, I thought you might like to play with this problem yourself.  For the competition the students got exactly five minutes to come to their answer, but I’m sure it will occupy far more of your time than that – it’s addictive!

So the great thinkers at Mathnasium had the idea of having a tie-breaker that would test the creativity of each mathematician…

Here’s the problem: Use only the following two numbers, 3 and 8, and the operations, parentheses, exponents, multiplication, division, addition and subtraction to make a number as close as possible to 100 without equaling 100.  3 and 8 may each be used more than once, but only as a single-digit whole number (so you can’t use “88” for example).  Each operation may be used more than once as well.

Here are a few possible answers, each getting closer and closer to 100:

(3+8)*8=88

(3+8)*8+3+8=99

(3+8)*8+3+8+3/8=99.375

(3+8)*8+3+8+3/8+3/8=99.75

(3+8)*8+3+8+3/8+3/8+3/8=100.125

(3+8)*8+3+8+3/8+3/8+3/8-(3/8)^3=100.072266

You can see that this would show who really is the quick, creative thinkers, can’t you?  You can try it with different digits or try it without starting at the same place each time.  And if you still have a tie in your house, try it with two different digits and get as close to zero as you can without equaling zero!

You’re welcome!  Something fun to do over Thanksgiving break!