Here's a lottery-themed variation of a puzzle I saw at work a while back.
Your lottery retailer has a crazy new kind of customer ticket scanning machine that works like this: You have to put at least two scratch offs inside it, and then the machine will display a number that is either the sum of the prizes or the product of the prizes. (Assume prizes amounts are whole number dollar amounts, e.g., 0, 1, 2, etc.)
You don't get to choose whether it gives you the sum or the product; the machine randomly chooses for you. The machine display does not say "sum" or "product" when it gives you the number, but it does make two different beeping sounds depending whether the number displayed is the sum of the product. Unfortunately, your retailer forgot which beep sound means sum and which beep sound means product!
Despite all these annoying details, the person in front of you in line decides to use the scanner a couple times.
First, he puts in three scratchers and the machine displays "36" making a high-pitched beeping sound. Then he takes them out and puts back in two of his three scratchers. The machine then displays "13" making a low-pitched beeping sound. You can't see his tickets to gain any more information.
Can you figure out the prize value of at least one of his three tickets?