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Can't see why not. Which way round are you thinking of doing it?
I'd probably do the Newtown bit on the way to Chepstow first and then look to sleep somewhere around Rhayader (B&B maybe with late arrival) on the way back but I haven't looked at the distances properly. I'll grab the perm routesheet and have a nose.
Either way I'd be looking at where ~400km puts me (assuming a 6am start like the calendar event) and see if there's a way to fit a sleep stop in there. Otherwise I'd just push through and nap somewhere just before sunrise.
I can imagine it's a tough perm (I've only done the calendar event) given the lack of 24 hour facilities en route, but it is a lovely route.
Can any BCM vets think of a reason riding it as a perm but starting ~Bangor would be a bad idea?