Disclaimer. The practical execution of the algorithm in question might be illegal in certain jurisdictions, and is thus strongly discouraged by the poser of the problem.
This recent post on the Muffin problem made me think of the following question.
Can we cut 100 banknotes into pieces of size at least $10\%$ each, and reassemble them into 101 banknotes of size $100\pm2\%$ each?
So each original banknote is cut into at most $10$ pieces of substantial size, and each new banknote also consists of at most $10$ pieces. The patterns on these newly formed banknotes should match, so we also demand, say, that no part of a banknote appears twice on a new banknote. Of course, these numbers are quite ad hoc, I'm happy to see any similar result. Note that if we don't require each piece to be at least $10\%$, then it is easy to make the trick by cutting each banknote into only two (sometimes very unequal) parts. I also wonder if non-vertical cuts might help, but I would like to keep the pieces simply connected regions bounded by Jordan curves.
Also, is there some implication between this question and the Muffin problem?