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On what surface and what type of 100km?
I would use a very different 23C for a fixed gear crit vs. a fixed gravel ride. Silly example but you get the idea.
If the roads are UK roads and speed isn't an issue I'd run a Durano or maybe a Michy Endurance. If I wanted something a bit quicker I still have 23C Rubinos kicking around, cobbles I'd use Paves, GP4000S are quick.
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This is my point though. If you're not skidding the question may as well be "what tyres should I use to ride 100km?" The answer is dependent on all the standard variances that go into tyre choice and have nothing to do with having a freewheel or not.
Cost, durability, plushness, grip in the wet, fastness, lightness, do i have one in the shedness....etc. It's just a 100km spin around some roads - don't over think it.
Say hypothetically you had to ride 100km on a fixed gear. And said fixed gear was limited to 23c tyres. What tyres would you be looking at?