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I was at a local bookstore the other day, and noticed a small toy. It was a customizable Sonic Screwdriver from Doctor Who. It had 3 screwdrivers, each with 3 interchangeable components. On the box, it proclaimed in bolded text: "OVER 80 COMBINATIONS."

Wanting to see if the company who had created this label was lying, I did some math. Figuring it was like a base 9 combination because there were 9 parts, I realized 9^3 was waaayyyy over 80. Then, I realized that each of one part had to be present, so I worked out in my head and thought that it would be more like a base 3 number combination, 0 representing a part from the first screwdriver, 1 representing one from the second, and 2 representing one from the third. Then, since there were three parts total, you could work it out with 3^3, resulting in 27. So, my question: was it lying when it said that there were over 80 combos, or is my math wrong?

Thanks in advance, Joe

joeelectricity
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1 Answers1

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Your description doesn't quite make clear how the toy works, but suppose it has three "base" objects, each with slots to attach three types of accessory -- and for each of these types of accessories there are three different accessories that match the slot.

Then the total number of completed configurations is $3^4=81$, with one factor of 3 corresponding to the choice of base, and a factor of 3 for each type of accessory.

And 81 is indeed OVER 80.

hmakholm left over Monica
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  • And the marketing people know that putting "OVER 80 combinations!" on the box sounds like a much bigger deal to the prospective customer than just writing "81 combinations"... :) – colormegone Feb 03 '14 at 03:49