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 Zachâ€™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?

(In reply to

Why I'm with Ady by Jer)

The process described by Jer is exactly what I have experienced.

I believe it took me less than 20 seconds:

Anyone used to fiddle with numbers( including myself) **knows** that 2*6 and 4*3 are the **only** sample within the nine non-zero digits of of two distinct couples (a,b) & (c,d) that produce the same result when multiplied, and in the same time the sums have opposite parities.

Thus it boils down to mentally evaluate** 1*5*7*12=60*7=420**.

I estimate that I've spent over 5 min. trying to justify myself by typing the above..

But, to quote Jer, it was a **TOURNAMENT** (sic!) question!