Sunday, March 10, 2013
Ping Pong Redux: A Visual Representation
Before reading this post, you might want to read my previous post on Ping Pong Redux since below is a solution of sorts. Another option, though, is to not read the previous post and instead attempt to backwards engineer the problem. I'd be curious what people came up with (and if the fact that you know the name is too constricting). I'll leave out a key for now.
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Unfortunately I already had read the original post before seeing this one, so I already knew what the grid represented.
ReplyDeleteI don't understand the color coding here entirely. In particular, there's blue (that looks synonymous with red) and then there's that light Bianchi-green sort of color that also looks synonymous with red. And then I think I finally figured out what determines which cells labeled with ordered pairs get colored yellow as opposed to white.
This is a fun game, for sure! And the idea of representing it as a grid like this is very nice. After all there are only 441 squares here, so that's not so bad. But ... wait a minute ... what about the row and column that ought to be labeled 0? Hmmmmm.
Spoiler alert...
DeleteI didn't include the 0 row/column because...nope, no excuse. Just an oversight. :) As for the coloring, the red represents scores you cannot reach, the dark green represents scores you can reach without a previous reduction and where there is an endgame path that does not involve a reduction, yellow represents scores that will inevitably lead to a reduction, light green represents scores that can only be reached by a previous reduction and will inevitably lead to another reduction, and blue represents scores that can only be reached by a previous reduction but have at least one clear endgame path.
As I was thinking about this recently, another question occurred to me: What is the longest game you can play without having the same score twice?
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