On the other hand, if the interviewer says "ok, just quickly talk me through an outline of the solution to this one first", you look like you can't answer the question, and also like you were lying to cover it up.

The optical mouse I used on a Sun 3 in the late 80s required a specific surface (reflective, with blue stripes one way, yellow the other, though AIUI for the yellow of it was infra-red reflectivity that actually mattered).
But the Xerox mouse our documentation team used at the same time was less fussy. It came with a specific mat, but would work on a black and white photocopy of it, and on any surface with a more or less regular texture, like the leg of a pair of jeans. (But not on a plain white desk.)

Except that doesn't preserve (ratios of) lengths, so it's not so helpful finding the longest route. It also shows at most half the surface (and needs an infinite map to do that).
No projection preserves both lengths and angles; the globe and string is a better suggestion.

Yes - the longest _land_ route, which the article is about, does have one end near Sagres, Portugal, but the quoted text is describing the longest sea route.

If you can persuade the court that you really don't have the password or decryption key they asked for, then it's not an offense not to provide it.
If you really have forgotten it but the court concludes that on the balance of probabilities you are lying about that, _then_ you are boned. Especially if there really wasn't any child porn on your computer and remembering the password would have let you prove that.

If you are in a game where you are playing/betting against other players, not just the house, and you are better than the other players by more than the house margin, then you can win in the long run. Many of the people who think they are in that situation are idiots, but it is possible.