Solutions for Act IV Scene 3 - DNF

The first step here is to realise that each shape is in fact the shape of a racing circuit. This is hinted at by the title, which means "Did Not Finish" in racing jargon. Further research reveals all the circuits supplied are being used in the Formula One races this year.

Furthermore, this gives us an ordering of the circuits, which must be used to extract the final answer. Before doing so though, we'd like to untangle the current mess we've been shown. Close inspection reveals there are five distinct loops of four circuits each hidden in the shape, which appear as follows (with their associated 2012 racing order numbers attached):

Note each chain gives us an arithmetic sequence. Following the title's hint that these sequences haven't finished, we can assume the next step is to work out the next number in each case. In all cases we want to traverse the chains clockwise, as evidenced by those in which only one direction works. Altogether we get the numbers (clockwise from the top) 1, 21, 2, 5, 19.

Next we need to notice that these five chains in fact make up their own mega-chain, as can be seen here:

This implies that we have one more sequence that hasn't been finished. There's no logical mathematical ordering to this sequence, but if we substitute the letters for numbers we get a promising string: SAUBE. A quick Google reveals there is only one appropriate letter that can end this string to give a thematic answer: appending an R gives SAUBER, a Swiss Formula One team.

The answer is: sauber