That is correct captaincoma. Thanks to Oyler for a wonderful puzzle - the trickiest number puzzle for a while...wonderful to have one which cannot be brute-forced on a computer and where there is a logical path without any guesswork or trial-and-error and just lateral thinking. (btw also congratulations to Fibonacci!)
I made the same initial assumption, with the same result of course. Then read preamble carefully, all OK now. Enjoyed this a lot, soluble with pen, paper (the back of my initial print out) and a couple of number tables. Loved Fibonacci!
I prefer the puzzles which illustrate a topic in number theory, but this one worked out with pen and paper without too much difficulty. I did make an assumption on student numbers which probably should have been included in the preamble.
This was pretty fiddly, but I loved how Oyler added a story to a numerical puzzle. It was surprisingly difficult for my metric-centred brain to use a perimeter in yards and a speed in feet per hour to a time in seconds!
Finished, I think, but have to say Pheidippides can travel at some speed, a snail on steroids perhaps - certainly much faster than my brain was working.
I too thought the way the puzzle was set out was quaint and not without humour.
It was unexpected to be able to deduce the wife's code so early on in the problem -- I was presuming it would have been one of the last things to do! Although I guess the Master of the college would want to obtain the code fairly early on without having to deal with snails!
Good fun - albeit I made a schoolboy error which derailed me for quite a while - amazing what a quiet nap with the problem rolling around the brain can do though. I liked the way that three logical entry points gradually converged (or failed to meet, in my original attempt).