International Mathematics Competition
imc-math.org.uk
imc-math.org.uk
The link has past problems with solutions; they are not quite at Putnam level, but they still pose a good challenge and tend to be very interesting.
This year apparently the competition will be held in Blagoevgrad, Bulgaria, at the American College. I am very close by in Thessaloniki, so if someone is participating and wants some face to face problem solving, let me know.