Your update is completely wrong. '123' =~ /(.*)(\d)/ will match just fine. If .* matches too many characters for \d to match, backtracking will occur causing .* to match fewer characters.

'123' =~ /(.*)(\d)/      (12)(3)
'123' =~ /(.*?)(\d)/     ()(1)

'a123z' =~ /(.*)(\d)/    (a12)(3)
'a123z' =~ /(.*?)(\d)/   (a)(1)
[download]