🎓 Doc Freemo 🇳🇱 @freemo@qoto.org

@freemo Found it! https://www.youtube.com/watch?v=KwawsVan05s

@timorl Correct, I'm very impressed :)

Rule number one to solving any problem: use graphs (as in Graph Theory)

@freemo

The jars with papers inside represent a permutation, every piece of paper points to the next jar in the permutation, say we number the jars from left to right. As all permutation, this one can be represented as a collection of cycles. Two key insights about these cycles:
1. Every cycle containing the jar numbered $k$ neccessarily contains the piece of paper with $k$ written on it, otherwise it wouldn't be a cycle.
2. At most one cycle has length greater than $50$.
With these insights the solution is simple. Your assistant looks at the whole permutation, and if any of the cycles has length greater than $50$ they switch the pieces of paper to break the cycle in half. They do nothing if there are no big cycles. Now you get told the number you are looking for and go for the jar numbered with it. Afterwards just trust the pieces of paper to lead you to the correct jar.

Thanks for this puzzle, solving it gave me a very needed confidence boost. *smugness incoming* Especially since I didn't even need to use paper.

"Be who you needed when you were younger" Speech from Brad Montague https://www.youtube.com/watch?v=KwawsVan05s

@freemo