Counting by the finger
What is the maximum number we can count to with increments of by using the five fingers on only one of our hands?
Details and Assumptions:
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When counting, each of the fingers is only either raised or lowered. Tilting, bending, or whatsoever maneuvers made don't constitute any other meanings or values.
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A finger combination may not have multiple values. For example, if raising all fingers counts to , then it can never be used for other numbers.
The answer is 31.
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1 solution
The maximum number is achieved when we count in binary. We will let 1 represent a raised finger, while 0 represent a lowered one.
Treating the individual fingers as place values for binary digits, with the rightmost finger being the rightmost digit (what finger this is depends on what hand you are using) we can see that our maximum becomes
2 4 + 2 3 + 2 2 + 2 1 + 2 0 = 3 1
I hope nobody gives me a 4 for this.