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Sol LeWitt's combinatorics

Sol LeWitt's combinatorics

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Tutorial

Introduction

Sol LeWitt was an artist who used geometry in some lovely, lovely ways.

The Walker Art Center in Minneapolis recently did a retrospective show on his work, titled Sol LeWitt, 2D + 3D. Included in the show was a set of pieces titled, Lines and Color.

The problem

The image below is part of the exhibit. It reads, "Straight, not-straight and broken lines using all combinations of black, white, yellow, red and blue, for lines and intervals".

The exhibit takes place on four walls of a single room. The question is, "Did he get them all?"

Or more precisely, since you cannot see the lines very well in the photographs below, the question is "Is it possible that he got them all, or might he have left out some possibilities?"

If you have not already read my packet on the Fundamental Counting Principle, now is the time to do so.

Just to make clear the artist's intentions. He says that he has produced all possible combinations of two colors (selecting from the colors listed), using each as a background color and as a line color, AND using each line color for straight, non-straight and broken lines.

If he did it, how many works of art should there be? And did he really do it?

Source: Photographs taken at the Walker Art Center, March 2011

Did he get them all?

First wall

Second wall

Third wall

Fourth wall

Source: Photographs taken at the Walker Art Center, March 2011

Solution

You may find my packets on the Fundamental Counting Principle and Nike combinatorics helpful in solving this task.

Feel free to post your ideas in the Q&A.