The way it was pitched to me was "this is so bad that during prohibition they let people still sell this because it tasted so bad".

My feeling is that it'll struggle with word-plays in OnlyConnect/Connections (like missing letters, added letters, words-within-words homophones, etc) as well as two-step references (such as {Venice, Dream, Night, Nothing} => "last words of Shakespeare plays"}).

* a "tail" -- some initial part of the path before you get into a true cycle (like the 002, 004 in the example above)

* an inner repeating cycle before you reach a node you've seen before.

In the case given |t| = 0 and |c| = 1, but it's easy to construct a more complex example with nodes (A, B, C, D), edges (A->B, B->C, C->D, D->B), and 'ending nodes' being B and D. In this case left and right paths go to the same node. This case would have a tail of length 1, and then the inner cycles would be of length {2, 1, 2, 1 ...}.

As a result, valid 'ending states' (Z-nodes) for this graph would be after {1, 3, 4, 6, 7, 9, 10, ...} steps.

The intended solution was seemingly to calculate the length of the cycle (as in, until you were on a "Z" node) for each starting node separately. Once you'd done this, you could find the LCM of these cycle lengths to find the overall period of the cycle (~10^13).

This solution might not work if your cycles weren't constant length -- for example imagine when walking your graph you found your i_th Z-node after {6, 7, 6, 7, 6, 7, 6, 7 ...} steps; or perhaps {6, 7, 7, 7, ...}. In the test data, this didn't occur - it was always {n, n, n, n, ...}.

I can give another example perhaps - consider you're asked to find the last 3 digits of 2^n for n >= 1. You start off calculating: 002, 004, 008, ... eventually you get to 2^103 which ends in 008. This means that the cycle length would be {103, 101, 101, 101, 101, ...} since it'll never get back to 002 or 004. Solving this is a bit more difficult than the constant cycle lengths, since it's not a simple LCM.

That's a very nifty strawman, but that's not my claim (at least not in such a general way). In this case it's become SOP by experts in a field, specifically for safety reasons. Other experts in the field have said "well, we don't think it's necessary - there are downsides such as aircraft landing rate". These groups of experts don't disagree on the fact that it's more safe - they just disagree as to what the optimal combination of (safety, financial value) is appropriate.

Apparently some Canadian carriers do also have this as a SOP.

Around the time this happened I spoke to some friends who are ATCs (in the US) who all immediately agreed it was a very reasonable request, especially given that the request was made far enough out (so it wasn't like they'd have to quickly scramble to respace the incoming planes correctly in the sequence).

I'm actually surprised SFO still allows visual approaches at night after that Air Canada 759 flight nearly landed on the taxiway ~5 years ago (https://www.youtube.com/watch?v=aGQlQFn0euI).