For several years now, I have been collecting interesting problems that I have thought of, come across, or been told about. For many of these problems, I have written letters to a friend asking for thoughts. For some of them, I have written some programs and made OEIS sequences. For a few, I have come up with some interesting new ideas.
In late 2017, I started cataloging these problems, and by January 2018, I had written down 63 of them in a notebook. On December 11th, 2018 I removed about a dozen of the less interesting problems and started a version 2 of the collection.
This project is an attempt to catalogue all of the problems that I've been thinking about and help me to not forget about them.
If you're interested, here are some things you can do to help:
- Let me know if you spot any typos or ambiguities.
- Author an OEIS sequence related to a problem. (And let me know about it!)
- Send me an email if you see that I haven't contributed to this project in a while.
- Submit pull requests with links, references, examples, or solutions.
- Add related questions.
One of my earliest questions is related to the number of ways to weave coffee stirrers in such a way that they form a self-supporting structure, where removing any coffee stirrer results in the structure collapsing. I remember learning about one of these (5 stirrer) weaves when I was in elementary school, and I have since wondered what sorts of other configurations exist.
The unique configuration with 4 sticks (up to reflection).
More details about this problem can be found in v2/004_problem.pdf.
In February 2018, I met my goal to typeset problems 18–47. In July 2019, I added problem 100 (version 2).
- Problem 3 (V2)
- Problem 5 (V2)
- Problem 10 (V2)
- Problem 11 (V2)
- Problem 12 (V2)
- Problem 13 (V2)
- Problem 14 (V2)
- Problem 15 (V2)
- Problem 16 (V2)
- Problem 17 (V2)
- Problem 18 (V2)
- Problem 19 (V2)
- Problem 20 (V2)
- Problem 22 (V2)
- Problem 23 (V2)
- Problem 27 (V2)
- Problem 28 (V2)
- Problem 29 (V2)
- Problem 30 (V2)
- Problem 35 (V2)
- Problem 43 (V2)
- Problem 46 (V2)
- Problem 47 (V2)
- Problem 50 (V2)
- Problem 56 (V2)
- Problem 59 (V2)
- Problem 62 (V2)
- Problem 70 (V2)
- Problem 83 (V2)
- Problem 86 (V2)
- Problem 95 (V2)