Boxing Match

Dan and Dave are packing up orders at the Art of Play warehouse. Dan presents Dave with three boxes and asks him to print out shipping labels. Dave asks, “How much do they weigh?” 

Dan smiles and replies, “The sum of their weights is your lucky number.” Dave sighs. 

“I need more specifics.” Dave says.

“OK,” says Dan, “the product of their weights equals seventy-two.” Dave thinks for a moment. 

“That’s still not enough information.” he says as he looks around for the scale. 

“Hold on,” says Dan, “I have one more clue: the heaviest box contains my favorite thing in the whole store.”

Dave counts on his fingers for a few moments, then types up the shipping labels and places the correct postage on each package.

What are the individual weights of the three boxes?

Solution: First you need to figure out the various sets of three numbers that multiply to 72. When you look at the list of products and then compare their sums, you notice that two sets of numbers equal 14. This must be the lucky number because we still need more information to solve and any other total is a unique set of three. The last clue tells us there is a "heaviest box" which means the set can not be 6-6-2 and must be 8-3-3.

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