This article is from the Douglas Adams FAQ, by Nathan Hughes firstname.lastname@example.org with numerous contributions by others.
(This from Christ van Willegen)
In an interview, published in 'Mostly Harmless' (The ZZ9 club magazine), DNA
mentioned that he had made a puzzle that depicted 42 in 10 different ways.
Here's the solution:
There are 6 rowes of 7 spheres, making a grand total of 42. On the left is a
white globe with a bar code on it. 4 lines have no thick line next to them, 2
Next, all 7 lines of the diagram can be read as: 0101010, which is 42 in binary,
White, blue, green, 'light yellow' == 0
Red, purple, 'dark yellow', black == 1
Finally, if you take only the blue, green, purple, and black spheres, they
spell '42' in quite big letters. Exactly 10 ways to solve the problem!
(From Douglas Adams, in his speech to Washington University):
Bar Code = 42
Earth in bottom right corner [= "42"]
spheres with red tint (orange, red, etc) = "1", spheres w/o red = "0"
gets 0101010 lines = "42 in binary"
spheres with blue tint gives a big "42" across the whole puzzle
spheres with yellow tint gives a big "XLII" across the top of the page
He didn't mention the "10" solutions, just that he fit in as many as were
humane to include.