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Sol-ve this LeWitt Puzzle

The large geometric Sol LeWitt piece in the new temporary exhibition Lewis Baltz: Prototypes gave me an idea for yet another puzzle.  This one tests your research and math skills.  You can (and should) complete this puzzle online, although I strongly encourage you to come see the Baltz exhibition, and the LeWitt piece, in person.  The puzzle:

1.     Sol LeWitt's Nine-part Modular Cube consists of a three dimensional grid of cubes 9 squares high, 9 squares wide, and 9 squares deep.  How many different cubes of any size can be found in the piece?

HINT: Figure out how many cubes there are of each possible size 1x1x1 (729 cubes) through 9x9x9 (1 cube), and add them all up.  An additional hint may be found near the end of this document.

2.     Taking the answer from Question #1 (let's call the answer "n"), find the name of the artist associated with the nth piece acquired by the Art Institute in 1922 for its permanent collection.

HINT: Once you know how the museum’s accession numbers are formed, courtesy of Annie M., then you can perform a search using the museum’s online collections website.

3.     Taking the answer from #2, find the number of pages in a 1992 book about that artist in the Art Institute’s library.

HINT: The museum’s Ryerson and Burham Libraries have an online catalog.

4.     Taking the answer from #3 (let's call the answer "x"), find the title of  xth piece acquired by the Art Institute in 2008.  Finally, for the win, who is the lead actress in the 2004 movie of the same title? Leave it in the comments!

Sol LeWitt. Nine-part Modular Cube, 1977. Ada Turnbull Hertle Fund. © 2008 The Estate of Sol LeWitt.