How many cardboard digits do I need? I need to prepare digits made of cardboard to display some number (example). I don't know beforehand which number I should display - the only thing I know is that it's not greater than n.

How many cardboard digits should I prepare?

Example: n = 50

To display any number in the range 0...50, I need the following digits:


A zero, for displaying the number 0, or any other round number
Two copies of digits 1, 2, 3 and 4, for displaying the corresponding numbers
One copy of digits 5, 6, 7 and 8, for the case they appear as least significant digit in the number
The digit 9 is never needed, because I can use the inverted digit 6 instead


Total: 13 digits

Test cases (each line is a test case in the format "input; output")


0 1
1 2
9 9
11 10
50 13
99 17
100 18
135 19
531 22
1000 27
8192 34
32767 38
Jelly, 9 bytes

‘ḶDœ|/ḟ9L


Try it online!

How it works

‘ḶDœ|/ḟ9L
‘Ḷ         [0,1,...,n]
  D        convert each to list of its digits
   œ|/     fold by multiset union
      ḟ9   remove 9
        L  length