The Abacus Puzzle is a puzzle present in version 5.2 of Ao Oni. It is often noted for it being difficult for non-Japanese players due to it being a traditional Japanese puzzle. It is accessible after solving the Length Puzzle and obtaining the cipher. Solving it gives the code for the basement door.
ExplanationEditThe cipher is a sheet of paper with 12 black dots with the word PASS at the top. Under each of the letters in PASS there are 4 black dots. Imagine a line splitting the 4 black dots at the top from the 8 below them (It is easier to insert them into the frame of where the map used to be if you are having trouble imagining a line). Now look at the spaces where the dots are missing at the top. Any missing dots at the highest rows represent the number 5, and any missing dots on the lower row represent 0. Now look at the missing dots below the line. Any missing dots on the first row below the line represent 0. Any missing dots on the second row from the line represent 1, and so on. Now add P`s missing dots together, A`s missing dots together, S`s missing dots together, and S`s missing dots together. Line those numbers up in place of PASS to give you the basement door code.
An easier explanation can be found here http://browse.deviantart.com/art/Ao-Oni-cipher-help-242542649