Programming with DNA
Step 1: Create a unique DNA sequence for each city A through G. For each path, for example, from A to B, create a linking piece of DNA that matches the last half of A and first half of B.
In a test tube, all the different pieces of DNA will randomly link with each other, forming paths through the graph.

Step 2: Because it is difficult to "remove" DNA from the solution, the target DNA, the DNA which started at A and ended at G was copied over and over again until the test tube contained a lot of it relative to the other random sequences. This is essentially the same as removing all the other pieces.

Step 3: Going by weight, the DNA sequences which were 7 "cities" long were separated from the rest. A "sieve" was used which allows smaller pieces of DNA to pass through quickly, while larger segments are slowed down. The procedure used actually allows you to isolate the pieces which are precisely 7 cities long from any shorter or longer paths.

Step 4: To ensure that the remaining sequences went through each of the cities, "sticky" pieces of DNA attached to magnets were used to separate the DNA. The magnets were used to ensure that the target DNA remained in the test tube, while the unwanted DNA was washed away. First, the magnets kept all the DNA which went through city A in the test tube, then B, then C, and D, and so on. In the end, the only DNA which remained in the tube was that which went through all seven cities.

Step 5: All that was left was to sequence the DNA, revealing the path from A to B to C to D to E to F to G.

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