I know $# is the number of positional parameters in bash. But how does bash interpret ${##}? Here, is a sample output from my system.
$ echo $#
0
$ echo ${#}
0
$ echo ${##}
1
$ echo $##
0#
$# is the number of positional parameters, and ${##} is the length of $#'s value in characters; in other words it's the base 10 logarithm plus one, rounded down, of the number of positional parameters. $## doesn't work because it doesn't comply with the parameter expansion syntax.
Observe:
$ bash -c 'echo "$# ${##}"' _ {1..9}
9 1
$ bash -c 'echo "$# ${##}"' _ {1..10}
10 2
$ bash -c 'echo "$# ${##}"' _ {1..100}
100 3
See Bash Reference Manual § 3.5.3 Shell Parameter Expansion for further information.
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