Many years ago I picked up a little book by J. E. Littlewood and was baffled by part of a question he posed:
"Is it possible in 3-space for seven infinite circular cylinders of unit radius each to touch all the others? Seven is the number suggested by counting constants."
It is the bit in italics which baffled me then (and still does). Can anyone explain how he gets 7 by "counting constants"?
P.S. For completeness, the book is "Some problems in Real and Complex Analysis" (1968)