*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?