# Curio #123

October 2016

## Problem: Blue Dark

Figure 1: A lovely game of Pacman

## Initial Thoughts

A history of retro gaming helped me with this one. Anyone who has ever played Pacman knows the goal. Avoid the not so friendly ghosts Blinky, Pinky, Inky and Clyde while collecting all dots on the screen. The screen capture presented here is a an impossible situation; there are many strings of dots missing (rather replaced by small dots) that could not be eaten without other some of the uneaten dots also missing. This implied that the message was encoded in the dots, likely in binary with the two states small and big dots.

## Following Process

After my initial thoughts, I considered ways in which the dots should be ordered. By row or column. Then it dawned on me that you could not resist using the elements of this unique medium. So I was certain the order of the message was determined by a Pacman path through the labyrinth. I was happy to find that there existed only a single, non-intersecting path from our Pacman hero through all the strings of small dots. This path also concluded right on Blinky, a good sign. The fact that the longest string of large dots on this path was 4 while the longest string of small dots was 11 suggested that the large dots were 1’s and the small dots were 0’s with 0 strings of a certain length corresponding to spaces. Upon counting the length of the Pacman path and finding it to be 135, I determined letters could be determined by strings of length 5. I was frustrated at first to find no reasonable message despite what I thought to be good rationale. I realized my silly (sadly frequent mistake) with binary, that is reading backwards. 10000 → 16, not 10000 → 1. Upon correcting this error, I uncovered the message.