CG has a correct and accepted answer, as verified by a python program I wrote that generates all possible chains over the range 001...360.
Shown below are examples of solutions for other ranges of numbers, in a form that shows chain length, the chain's maximum value, and solution(s).
C2 10 [(2, 3), (2, 5)]
C3 21 [(2, 5), (2, 7), (3, 7)]
C3 21 [(2, ...
I think it's a safe assumption that the answer will be of the form:
The reasoning is that
Now, we want to get the longest sequence. To achieve this
For instance, if we try
Let's try another:
Going even lower is not an alternative, since:
Without a rigorous proof I'm going to say the combination is:
This is a very interesting puzzle. I am not sure how to approach it rigorously, other than applying the deductions already mentioned, therefore I did a lot of trial and error. I have not come up with a solution yet, so I will keep trying, but I thought I'd share my progress as there have been no new developments on this problem for some time. Here is my ...