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Question: 

A few extraterrestrials arrived. They had two hands, but claimed that 3 + 2 = 11. How many fingers did they have on their two hands? Note that our decimal system (and ten characters: 0, 1, 2, $\dots$, 9) surely has its origin because we have ten fingers. [Hint: 11 is in their system. In our decimal system, the result would be written as 5.]

Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014. Reprinted by permission of Pearson Education Inc., New York.
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Quick Answer: 

2 fingers on each hand

Giancoli 7th Edition, Chapter 17, Problem 64

(0:44)

Chapter 17, Problem 64 is solved.

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Transcript for this Giancoli solution

This is Giancoli answers with Mr. Dychko. Having the number one one represent the decimal number five means that they must have a base four counting system where this digit represents four to the power of one. And this didit here represents four to the power of zero. So four to the power one plus four to the power of zero makes 5. And so that would be consistent with having a total of four fingers or two fingers on each hand. Just like with our our base ten system we have, we have a… total of ten fingers or five fingers on each end.