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Words count (Posted on 2014-03-25) Difficulty: 4 of 5
(D3)How many subsets of (a,b,c, x,y,z) contain no letters neighboring each other in the English ABC (26 letters)?

(D4)How many "words" (i.e, ordered subsets from (a,b,c, x,y,z)) contain no neighboring letters that neighbor each other in the English ABC (26 letters)?

No Solution Yet Submitted by Ady TZIDON    
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re(2): Solution | Comment 3 of 8 |
(In reply to re: Solution by Jer)

1
1  1
1  2
1  3  1
1  4  3
1  5  6  1
1  6 10  4
1  7 15 10  1
1  8 21 20  5
1  9 28 35 15 1

claims that for a 3-letter alphabet there is only 1 2-letter word, but there are actually 2: ac and ca. For a 4-letter alphabet it says there are 3 words of 2 letters, but there are 6: ac, ca, ad, da, bd, db. It lists no 3-letter words for the 4-letter alphabet, though there are 4: adb, bda, cad, dac.

My own table (more forthcoming in another post) looks like:

1      1  1                                      
2      1  2   0                                   
3      1  3   2    0                               
4      1  4   6    4    2                          
5      1  5  12   18   20    14                    
6      1  6  20   48   90   124    90              
7      1  7  30  100  272   582   860   646        
8      1  8  42  180  650  1928  4386  6748  5242

 


  Posted by Charlie on 2014-03-25 15:39:29
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