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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(3): Solution Comment 8 of 8 |
(In reply to re(2): Solution by Charlie)

My chart is wrong, just not in the way you pointed out.   My chart if of "subsets" not "words."  I then multiplied each number by n! to get the number of words.

The disagreement is how I interpreted "no neighboring letters that neighbor each other."   I discounted words like adb which contains a and b -- neighboring letters even though they don't neighbor each other.

My solution is then to the slightly simpler problem: 
How many "words" (i.e, ordered subsets from (a,b,c, x,y,z)) contain no neighboring letters in the English ABC (26 letters)?


  Posted by Jer on 2014-03-26 09:21:08

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