## 12.LAb[au] (BE)

### One of a Billion Weeks

##### 201628 black A1 frames, 7 hard cover A4 books, light object, generative software

One 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.