Propagating Errors

Jim mentioned Puzzled Pint a few months ago, but it conflicted with an improv rehearsal. However, this month, we decided to make Puzzled Pint our troupe’s social outing.

The first step in Puzzled Pint is to figure out where the event will be held. To do this, one solves a location puzzle. In our case, we needed to traverse a maze, and the puzzle was sensitive in the sense that early mistakes propagate to steps later on. It took a while to realize that we had missed a clue, but once it was resolved, we found ourselves on our way.

What’s interesting about a puzzle with this type of propagating error is that it becomes fairly simple to detect that an error was made since the solution is typically an English word or phrase, but not necessarily obvious what the error was, akin to losing an inter frame in video and seeing an error propagate across subsequent frames until the start of the next GOP. The difference between the puzzle and video coding is that given a codec, there is a well understood way to decode the video frames, whereas in the puzzle, the decoding mechanism is intentionally obfuscated and to be deduced along with the solution.

This makes a mistake in a puzzle all the more challenging to debug. For instance, in an early attempt at the February location puzzle, I decoded ROTATERETAMETOYONE, so I was confident that my method was on the right track because the prefix ROTATE is a word, but it wasn’t necessarily clear whether I was applying a correct method and had simply overlooked a piece in the process, or whether the method I was applying was too simplistic to solve the puzzle, and there was something more complex occurring that needed to be applied before moving to the next word.

Ultimately, someone figured out what was missing, and we had a mechanism to validate that the solution we had arrived at was correct. That leads to a second difference between video coding and puzzle solving; namely, it’s sometimes possible to arrive at and validate a solution by sidestepping the expected method the puzzle wants one to apply. For instance, if one gets enough clues that the entropy of the solution is sufficiently low, taking advantage of one’s knowledge of English can provide an alternate mechanism to arrive at the solution instead of figuring out the intended method. In fact, in some cases, one might reverse-engineer the remaining pieces of the method after discovering the solution.

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