May 2002
Solution:
1)Center=(31.25,0), radius=31.25, points (0,0), (2,11), (2,-11), (40,30), (40,-30), (50,25), (50,-25)
Schinzel's theorem guarantees that this problem can be solved for any given number of lattice points.
2)The smallest such circle has center (5/22,9/22) and radius sqrt(276250)/22.
3)Vladimir Sedach and Hajo Luers each submitted a list of 65 circles with radius less than 50, each passing through exactly seven lattice points.
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