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To the south of city centre, you'll arrive at two cloverleaf interchanges, one giving access for the road to tiny village of Arifiye, and the other, about 1-2 km south of the first one, providing access to main Istanbul-Ankara motorway (O-4/E80, also known as Anadolu Otoyolu).
Start hitching in on-ramp of the second cloverleaf interchange. It shouldn't take long.
Walk past all on-ramps, keep walking until you pass a military area located just south of second interchange (they may make a fuss if you start hitching right in front of it), and start thumbing as soon as you see a nice shoulder. Vehicles are relatively rare here (especially if you are coming from Istanbul area) and they speed by quite fast, so how long you must thumb there varies, but most of the time first lift offer comes within 30 minutes. Also take note that recently built new motorway bypasses city of Bilecik about 5-10 km away, so if you are/are not heading for there, take this into consideration. You might get stuck in now-deserted old motorway out of Bilecik through the night! WikiPedia:Adapazarı