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)