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?
Best Answer
This (top half) is a way to cut 49 banknotes into pieces of at least 10% each and (bottom half) reassemble them to 50 "98%" banknotes. Let $w$ denote the width and $h$ the height. The bills below have an aspect ratio of 1:2 but this isn't necessary.
(SVG source code)
I hope that it's clear how the pattern continues in the center; simply use each leftover piece together with the next one (which is matching in color) to form a 98% bill; the size of the square gap is $\frac{w}{10}$ by $\frac{h}{5}$.
The two outer columns on both sides are trickier, because it's impossible get rid of the corners with the same scheme as used in the center. Therefore, we cut strokes with width $\frac{w}{5}$, moving $\frac{h}{10}$ downwards each time. Reassembling them gives 'inlets' of $\frac{w}{5}$ by $\frac{h}{10}$.
Note that all bills get cut into two pieces, except for the two with the large light blue part (top left and top right) which are cut into three pieces.