I wonder how the $1 =~ tr/\n// in your solution doesn't die with "modification of a readonly value attempted"?

This special form of tr with an empty replacement list is used to count the number of characters. Example from perlop:

$cnt = tr/0-9//;            # count the digits in $_
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In perlfaq4, they give an example indicating that this idiomatic use of tr is the canonical Perl way to count the number of characters in a string. Admittedly, apart from these examples, I can't find an explicit statement in the docs that this special form of tr does not attempt to modify the string.