A sewage worker was tasked to go down a manhole to clean up a clogged pipe. At first it didn't seem like much, just another ordinary day on the job. He went down into the manhole truly expecting anything.

The sewage system was built like a labyrinth, murky and dark. He could have sworn he heard an It laugh from the shadows. Scared as a cat, he ran to the pipe placement, accidentally dropping the map in the sewage near the pipe. he wasn't going to risk looking for the map, it was probably disintegrated by now. He remembered a few things about his path though

  1. There were 10 turns in the path

  2. The ratio of right turns to left turns was 2 to 3

  3. There was a right turn at the beginning and end of the pathway to the clog

  4. The left turns came in groups of 3, separated by more than 1 right turn in between.

Can you understand the path he took from the entrance to the pipe? List the directions in order from the entrance to the pipe!


The sequence must be



1,2,3 tell us that we have RxR where x contains 6L+2R, and then 4 tells us that those six Ls split up as two groups of LLL, and that in between we have RR (we have only two Rs to provide "more than 1 right turn in between").

  • $\begingroup$ Ah, ha. I just typed out my answer, but I refreshed the page and your answer was there... nice. I assume @XavierStanton meant to say $R:L=2:3$ [EDIT:It was a typo, Xavier corrected] $\endgroup$
    – user46002
    Nov 5 '18 at 21:44
  • 1
    $\begingroup$ Yup -- and it's been fixed now. (I deleted a bunch of now-redundant comments about the typo.) $\endgroup$
    – Gareth McCaughan
    Nov 5 '18 at 21:45
  • $\begingroup$ Sorry again guys, I was typing fast $\endgroup$ Nov 6 '18 at 2:04

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