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For which arrangements of two infinite circular cylinders does their intersection lie in a plane?

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1233IMO Shortlist 1966 problem 500
1231IMO Shortlist 1966 problem 480
1229IMO Shortlist 1966 problem 460
1228IMO Shortlist 1966 problem 450
1227IMO Shortlist 1966 problem 440
1225IMO Shortlist 1966 problem 420