... a mathematical solution hiding in plain sight.

Perhaps better to say "hiding in obscurity." From the OP (emphasis added):

... find a missing number if in a list of numbers. ...

...
my @arr = (19,17,22,23,24,15,16,25..35);
...

But the list in the code example clearly has more than one missing number. See also the (current) thread title. I think the goose chase, although wild, was justified.