Day 312 #637

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1. vaskoz

   self-assigned this

   on Jun 30, 2019
2. vaskoz commented on Jun 30, 2019

   

   vaskoz

   on Jun 30, 2019

   OwnerAuthor

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   Writing this out by hand on paper showed that the pattern is Fibonacci. Below I've included the pattern worked out to N=5.

   N = 1, answer = 1
   
   1 # vertical only domino
   1
   
   N = 2, answer = 2
   
   12 # 2 vertical dominos
   12
   
   11 # 2 horizontal dominos
   22
   
   N = 3, answer = 3
   
   123 # 3 vertical dominos
   123
   
   113 # 2 horizontal dominos and 1 vertical domino
   223
   
   112 # 2 trominos
   122
   
   N = 4, answer = 5
   
   1234 # 4 vertical dominos
   1234
   
   1122 # 4 horizontal dominos
   3344
   
   1134 # 2 horizontal, 2 vertical dominos
   2234
   
   1123 # 2 trominos and 1 vertical domino
   1223
   
   1122 # 2 trominos and 1 horizontal domino
   1332
   
   N = 5, answer = 8
   
   11223 # 4 horizontal dominos and 1 vertical domino
   44553
   
   12345 # 4 vertical dominos
   12345
   
   11234 # 2 horizontal dominos and 3 vertical dominos
   55234
   
   12245 # 2 middle horizontal dominos and 3 vertical dominos 
   13345
   
   11234 # 2 vertical dominos and 2 trominos
   12234
   
   11233 # 2 horizontal dominos and 2 trominos
   12244
   
   11334 # 2 trominos, 1 vertical and 1 horizontal domino.
   12234
   
   11334 # 2 horizontal dominos and 2 trominos
   12244
   
3. vaskoz

   closed this as completedin #638on Jun 30, 2019