Thank you everyone for your excellent contributions. Well done trying by hand and I hope some of you had a look at trying different numbers on the geogebra applet here.
It seems like finding a long sequence really is a challenge no matter what numbers you use.
However ….
It is technically possible to choose four numbers that make an infinite sequence where you never end up at 0,0,0,0. The solution is very tricky to work with though and using a computer doesn’t even help because computers round numbers to a certain number of decimal places which messes up the result.
For an explanation and how to get to the solution have a look at this blog.
The next official challenge will be launched on Wednesday 19th of April … please enjoy the other puzzles on this site in the meantime.
Dear Mrs Fleming,
Thank you so much for the link to the blog. It was extremely interesting and I will try his proof myself.