The other day I was waiting for a train and had just popped into the nearby branch of Costa Bean for a coffee, when who should I run into but my old friend Megan and her partner Ricky, studying a travel brochure.
"Going anywhere nice?" I asked.
"We're planning to spend a few days to ride on this railway." Ricky replied, handing me the brochure. It was for The Diamond Of Wales Line. "The line's only recently been opened. I want to look round all the stations. So we've booked a hotel which is nice and convenient for the terminus at Abercydabra. We'll start there, then for each of the other stations, we'll take one train there, get off and have a look around, then get on a different train there, and so on until we get back to Abercydabra. We're going to visit all the stations."
I opened the brochure, which gave the timetable:
Abercydabra 08:00 16:00 Maenddygap 09:00 17:00 Brynpen Hill 08:12 16:12 Llanllewllwyd 09:12 17:12 Caerlesli 08:24 then 16:24 Kington 09:24 then 17:24 Dynower 08:36 16:36 Joneston 09:36 17:36 Egynbeicyn 08:48 every 16:48 Isicyl 09:48 every 17:48 Fforestffair 09:00 17:00 Hardllyr 10:00 18:00 Greenweli 09:12 two 17:12 Greenweli 10:12 two 18:12 Hardllyr 09:24 17:24 Fforestffair 10:24 18:24 Isicyl 09:36 hours 17:36 Egynbeicyn 10:36 hours 18:36 Joneston 09:48 17:48 Dynower 10:48 18:48 Kington 10:00 until 18:00 Caerlesli 11:00 until 19:00 Llanllewllwyd 10:12 18:12 Brynpen Hill 11:12 19:12 Maenddygap 10:24 18:24 Abercydabra 11:24 19:24
All trains are steam trains except the 10:00 from Abercydabra and the 17:00 from Maenddygap, which are diesel.
"That's not many trains per day and a lot of stations." I noted. "You're surely not going to manage to visit all of them in one day?"
"No, I don't think we can, but I want to work out an itinerary which minimises the number of days we'll need. Returning to our hotel at the end of each day."
"Of course! I'm not having us spending the night at a station!" Megan added. "Do the trains have dining-cars?"
"It doesn't look like it" her partner said, looking at the brochure again. "But I expect we can grab a bite to eat at a station café or somewhere near -- depending on where we happen to be at lunchtime. All the stations have cafés where we can have lunch."
"I'll want a proper lunch, what with all the train-hopping we'll be doing. So let's allow at least an hour for that, and not on a train. And at a reasonable hour, too, say some time between 12 and 2. Can you allow for that on our itinerary?"
"I expect so. Now I like steam trains but don't care so much for diesel ones. So let's see how we can do this in a way which minimises how much time we spend on diesels."
So, how many days will they need? And what will be their daily itineraries?
(I was inspired by this project.)
(Here's Geoff Marshall, with Vicki Pipe, explaining the specific bit which inspired my puzzle.)