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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40 comments

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Jesse Breazeale

3 lbs, 3 lbs, and 8 lbs

Jackie

My second guess is 3, 3 & 8

Jeremiah Dean

The weights of the boxes are 3, 3 and 8.

Jordan W. Dyk

4, 6, 3

Jackie Connelly

24 lbs each is my guess.

Justin Cunningham

2, 4, 9

Diego C.

Weight of three boxes: 4 – 9 – 2
Good Luck to everyone!

Georg Ye

I think the weight of the 3 boxes are 12,3,2, because their summ is 17 and I do believe that Dave’s favorite number has a 7 in it. And there are only 6 possible solutions( I believe) and 12,3,2 is the only combination where the summ has a 7 in it.

Alain Lacourse

The boxes weight: 2, 3, and 12

Dave’s lucky number = 17 (2+3+12)
Dan’s favorite thing is a brick of cards = 12
and 2×3×12 = 72

Gabriel smith

I think that it is 3,4,6

Dennis W

3, 3, and 8.

Matthew

18,18 and 36 :)

Joseph M

The weight of the boxes are 3, 3, and 8

Siddharth Rode

Further clarification on previous submission. Its 3-3-8 since of all the combinations of 3 whose product is 72, only 3-3-8 and 2-6-6 have the same sum. Of those, since the highest number is different, it must be 3-3-8.

Siddharth Rode

3-3-8

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