True, unless the starting tiles are messed up. E.g. like here
I haven't done the math myself and I'm not going to try digging into that but from what I understand start postions like that really are unsolvable.
I made an updated version (0410) to demonstrate what I mean. Download the new version. Click the Mission Impossible button and you get the teal coloured background and a supposedly unsolvable start mode.
The normal solvable modes are still there of course.
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