A problem from the 2004 Harvard-MIT Math Tournament:

Zach chooses five numbers from the set {1, 2, 3, 4, 5, 6, 7} and tells their product to Claudia. She finds that this is not enough information to tell whether the sum of Zach’s numbers is even or odd. What is the product that Zach tells Claudia?

I believe it is a d1 puzzle.

Are you on my side?

These tournaments are timed.  Speed and accuracy are both important.  Here's my reasoning when I first saw the problem.

Clearly the missing numbers aren't 5 or 7.  Ignore them.
What's left?  Ok by inspection with the pairs left you can make a 12 = 4*3 = 6*2 (odd sum vs even sum) or a 6 = 6*1 = 2*3 (both odd sums)
Since parity is unknown, some product of 12 is missing.

That leaves 7*5*6*2 = 420 by easy mental math
or 7*5*4*3  which is the same.

Elapsed time: less than a minute and I didn't have to write anything down.

I usually can't do math in my head without seeing the numbers or figures in front of me to start.  But seeing the number on the screen was enough.  If someone asks me verbally for that product it's hard to do be seeing them I can manipulate them in my mind.

If I was in this tournament I would then think:  "Wow, an easy one.  Now on to the problems I won't be able to do so easily, if at all."

Posted by Jer on 2016-03-07 10:47:25