Numberphile
2 HN recommenders · recommended in 4 months, 2018–2022
13:58 · 7M views · Oct 28, 2016
Numberphile with Daniel Erman on the Josephus problem, where people in a circle are eliminated in turn. It shows how the survivor's position follows a neat pattern tied to powers of two and binary.
HN cites it as an excellent example of solving small cases to find a pattern, and as a favorite puzzle with an elegant binary solution.
4 comments from Hacker News
Taking a break from sitting at the desk and going for a walk and thinking about the problem has worked surprisingly well for me many times. It was something I first read about in a Poincare's article on how Mathematical ideas are generated. Coming to general methods of problem solving in recreational math, I always look for symmetry and transforming the problem from one problem space to another and induction techniques before attacking it. For a research/modelling problem, my approach is to start working on the most simplified version of it and gradually progress towards the original problem. There is an excellent numberphile video on Josephus problem that illustrates how examining specific instances to observe patterns can help solve the general case. this video Edit: Formatting
I really like the Josephus Problem ([Numberphile‘s Video on YT]( this video )) because of the binary twist, really enjoyed Veritasium‘s [3x+1]( [LINK] ) and my favorite is your described [100 Prisoners Riddle]( [LINK] ) too
When I interviewed at my current company, I was pretty stressed about the interview and watched some Numberphile videos the night before to take my mind off things. Weirdly enough one of the problems discussed in the interview was about the Josephus problem which has a neat solution in binary [0]. I don’t recall if I ever asked the interviewer whether they also watched the video recently or how they came to think of it. [0]: this video
Simple examples may be useful. Exploring them, proving stuff about them it is how one may carve a foothold to solve a harder problem. Example: The Josephus Problem - Numberphile this video