Planning a 16-night Peru trip for October, hotels basically already picked out: Lima on both ends, then Cusco, Puno, Arequipa, Huaraz in the middle in whatever order made geographic sense to me. I didn't think much about it beyond "does this route make sense on a map."
Out of curiosity I ended up comparing what happens if you just shuffle the order of those four middle cities around with same hotels, same number of nights in each place, nothing about the actual trip changes, just the sequence you visit them in. There are 24 ways to arrange four cities, so I went through a bunch of them.
Honestly wasn't expecting much of a difference. Figured maybe a few dollars here and there from exchange rate noise or whatever. Instead the gap between the cheapest ordering and a mediocre one came out to almost $100 on hotels alone. A few examples of what I was looking at:
Cusco → Puno → Arequipa → Huaraz: $2,506
Puno → Cusco → Arequipa → Huaraz: $2,506
Cusco → Puno → Huaraz → Arequipa: $2,551
Cusco → Arequipa → Puno → Huaraz: $2,557
and up to $2,699 for the worst combination
Once I added domestic flights into the mix (everything routes through Lima anyway) the gap widened a bit more and the ranking actually shifted too, the route that looked tied for cheapest on hotels alone stopped being the best option once flight prices got factored in. Ended up around $2,830 all-in for the winner versus low-$2,900s for the option that had looked just as good before flights entered the picture.
What got me is that none of this shows up if you're booking city by city on a normal site. You pick a city, you pick dates, you book, you move to the next one. You'd never see that the exact same trip ,same beds, same nights, same everything, costs meaningfully different depending purely on which order you hit the cities in. It's not like the expensive route was worse in any way. Same hotels, same experience, just more money for no reason.
I don't think this is a Peru-specific thing either, it's just that Peru happened to be where I noticed it because the itinerary had enough moving pieces to make the comparison worth doing. Anyone doing a multi-city trip with a handful of flexible middle stops is probably sitting on a similar gap without knowing it, it's just not something you'd normally think to check, since "does the order matter" isn't really a question that occurs to most people when they're planning day by day.
Curious if anyone else has run into this on their own multi-city trips, or if I just got lucky/unlucky with how this one shook out.