## 12.

LAb[au] (BE)

*One of a Billion Weeks*

*2016*

28 black A1 frames, 7 hard cover A4 books, light object, generative software

28 black A1 frames, 7 hard cover A4 books, light object, generative software

O*ne of a Billion Weeks* demonstrates how a very simple construction, a combination of 18 elements, can generate myriad variations, and relates this fact to the concepts of time and information.

Visitors are able to visualise the possible combinations on a 10-character alphanumeric display. Each character is made up of 16 segments and 2 points that can be in one of two positions: on or off. As a result, there are \(2^{16+2}=2^{18}=262 144\) * possible unique results per character*.

With 10 characters, the number of possible unique results displayed is:

\((2^{18})^{10}=2^{180}\)

\(=1532495540865888858358347027150309183618739122183602176\)

If every minute one possible unique result is displayed than 1440 can be displayed in a 24-hour day, so 10080 in a 7-day week. Each of the 7 books in the work contains 1440 possible unique results.

*Combinatorics* is the branch of mathematics concerned with *counting*, both as a means and an end in obtaining results. It also studies properties of certain* structures* such as configurations of finite collections of objects.

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