Aw come on, i struggle with BBC2s Eggheads, im going for lie down after that clue!!
A161 near Carlton Miniott ? Nearer to Thirsk.
A67 darlington to barnard castle
god i thort people would of got it with the clue theres a dual carrigae way a few miles ahead and in june or september for 2 days theres qite a few trucks travel for a local event.
A68 near Barard Castle or Bowes Museum?
when the road goes onto dual carrigway 4miles or so you take the next exit turn right on roundabout you will end up by a zoo and funfair. but if you turn left at the roundabout you may bump in to a few ■■?'s trucks
Is it the A169 Malton to Pickering?
No sorry mick close. If you go the other way you probabally have a full taty bulker on and if you traveling in my direction you probally have a fridge on. One last clue i joined this road after loading tyres about 5miles down the road
A64 coming from scarborough towards malton (zoo & funfair would be flamingo land and the museum would be eden camp) if i am right. 
Well done katie its correct Its just coming out of rillington