Self-Reducing Bags of Digits
What if the numbers that we used were a finite resource? How would we describe how many numbers we have left, if we needed to use those numbers to state how many are left? What groups of numbers would we never run out of enough numbers to state how many are left? These strange questions and more are what we explore when we delve into the world of self-reducing bags of digits. Learn more at the links below, including the initial blog, visualizations of self-reducing bags from base 2-10, the pre-print of our paper proving that the number of self-reducing bags of digits is finite for base 2 and 3, and our GitHub repo for the project.
What even is a bag of digits? What makes them self-reducing? Why is the mathematics department running out of numbers? For an introduction to this puzzle, check out this blog.
Do you want to help with the search for bags of self-reducing digits? You can! Our GitHub repo contains the Python code needed to search for more. Will you be the first to discover another base with a finite number of bags?
Self reducing bags of digits form fascinating, almost fractal images when they are connected into a network. Check out these cool visualizations!
Want to see the proof that bases 2 and 3 are finite? Or maybe you just want a more formal statement of the problem and the process for investigating it? Check out the pre-print of the paper on Research Gate.
