# Solving Flip It, a Game

1. Nov 18, 2011

### TylerH

Solving Flip It, the Game

I've formulated the game Flip It(http://www.coolmath-games.com/0-flipit/index.html) into mathematical terms and a system of equations that solve for the solution matrix(the matrix of how many times each square must be clicked to solve from a given beginning.

Let $A_{5,5}$ be a matrix over the integers modulus 2 that represents the original pattern with 1 being white and 0 being black.

Let $M_{5,5}$ be a matrix over the integers modulus 2 that represents the matrix we want (to solve, this would be all 1's).

Let $B_{5,5}$ be the solution matrix, the number of times each square must be clicked, be defined by the equality $m_{x,y}=b_{x,y} a_{x,y}+b_{x+1,y} a_{x+1,y}+b_{x,y+1} a_{x,y+1}+b_{x-1,y} a_{x-1,y}+b_{x,y-1} a_{x,y-1}$.

How do I solve $m_{x,y} \equiv b_{x,y} a_{x,y}+b_{x+1,y} a_{x+1,y}+b_{x,y+1} a_{x,y+1}+b_{x-1,y} a_{x-1,y}+b_{x,y-1} a_{x,y-1} \: mod \: 2$ for all x,y in [1,5] (intersected with the integers, of course)?

Last edited: Nov 18, 2011
2. Nov 20, 2011

### TylerH

Re: Solving Flip It, the Game

I screwed up; both of those equivalences should be: $m_{x,y} \equiv b_{x,y}+a_{x,y}+b_{x+1,y}+a_{x+1,y}+b_{x,y+1}+a_{x,y+1}+b_{x-1,y}+a_{x-1,y}+b_{x,y-1}+a_{x,y-1} \: mod \: 2$

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.633073091506958, "perplexity": 1472.1718674166227}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267163146.90/warc/CC-MAIN-20180926022052-20180926042452-00122.warc.gz"}