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If I have 16 different symbols, how many of these symbols can I combine to create no more than 16.777.216 unique combinations?

Eg. I have all symbols of the Hexadecimal language (16).

How many combinations can I create with X amount of symbols to not have more than 16.777.216 unique combinations maximum?

The position of each symbol is of importance.

  • 1
    How many combinations do you get with 2 symbols? How many with $n$ symbols for $n\in\mathbb{N}$?2010-12-04

1 Answers 1

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Six, because $16^6 = 16.777.216$.

  • 5
    The statements about "what the poster needs", what "would much better serve him", what would "empower [him] to solve such questions himself", and the idea that this can "only be done by practice" are all presumptuous and highly debatable. The answer given is illuminating and may be exactly the hint needed to grasp the combinatorial idea involved. Practice is rarely useful when basic ideas are missing, it is an "empowerment" to run in circles. And it is not necessary to decide for the OP what is good for him or to impose such decisions on those who contribute on-topic answers.2010-12-06