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Colored triangle (Posted on 2018-12-14) Difficulty: 4 of 5
Begin with a finite sequence of blocks in a row, each in one of 3 colors: red, blue, yellow.

Below each pair of neighboring blocks place a new block with the color rule: If the blocks are the same color use that color but if they are different use the third color.


r b y y b
 y r y r
  b b b
   b b
How can the color of the last block be easily predicted from the top row?

Note: I don't know the full answer but can solve special cases.

No Solution Yet Submitted by Jer    
Rating: 4.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Complete formulaFrankM2020-08-26 08:28:03
The good parts (sketch of proof)FrankM2018-12-21 09:18:14
Some ThoughtsImplementation in Excelbroll2018-12-19 01:12:23
re: proposed solutionJer2018-12-18 11:07:19
re: proposed solutionSteve Herman2018-12-18 11:01:08
proposed solutionxdog2018-12-17 20:03:48
also, some random examplesSteven Lord2018-12-14 21:41:33
Some Thoughtsin case this helps guide the analysisCharlie2018-12-14 21:26:20
just a couple of off-the-wall ideasSteven Lord2018-12-14 17:52:01
Some ThoughtsOne obvious special caseSteve Herman2018-12-14 14:04:57
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