(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)?

(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