# RPS Trinity - Teddy and Her Ribbon

## The Rules of RPS Trinity:

• You are given a board with its tiles colored either black or white.
• Put Rocks (denoted by letter R), Papers (denoted by letter P), and Scissors (denoted by letter S) on white tiles so they appear exactly once in each row and column. It is clear that you don't have to put letter on all of the white tiles.
• You can't put the letter in a red-bordered tile.
• Same as the classic Rock-Paper-Scissor game, each can be represented by a hand with some of the fingers outstretched:
• Rock is a hand with 0 fingers outstretched.
• Paper is a hand with 5 fingers outstretched.
• Scissor is a hand with 2 fingers outstretched.
• Black tiles are walls and there is a number in some of them. These numbers are the sum of visible fingers outstretched seen from each of them.
• The tiles only see the first letter on their up, down, left, and right. The letters may block the visibility of the other letters behind them, so do the walls.

Ayu is only a little girl from a traditional village in Borneo island who really wants to make this Rp 59.000 (around 4 to 5 US dollars) teddy bear her best friend. Little do we know that she has a ghost of the past when she look at her red ribbon...

[the story may be continued later on next puzzles]

Finished:

Approach:

Not really much to describe here, other than some initial insights:

- The 9 block needs to be surrounded by one P and 2S. The right is no-go, so the first thing it sees on the left must be S, and up/down must be either one of S/P.

- The 5 block can only take one P. Based on the configuration of the row, the P must be visible from its left, so its up and down total must be 0. The only way for this to happen is for its column to have all of RSP above it, with R being the one closest to it.

- Similar approaches can be taken to the 0 blocks. The only way some of them can have a 0 total is for their columns to have all the letters above them.

- Coupled with many other similar insights, the solution can then be derived via elimination, no guessing needed.

• nicely done! :) Jan 18, 2018 at 10:35