4,3,5,4,3,6,8,7,7,__

Note : Think about the number of letters in some 'Numerical' (but English) words.

Ah!  I was looking at the sequence of five, nine, thirteen - maintaining a constant interval of '4' between groups of triplets.

Now if I use intervals that increase by 1, KS's sequence would therefore be:

4, 3, 5          five, six, seven                       
4, 3, 6          nine, ten, eleven                                      [4]
8, 7, 7          fourteen, fifteen, sixteen                           [5]
6, 9, 9          twenty, twenty-one, twenty-two                 [6]
11,11,10       twenty-seven, twenty-eight, twenty-nine     [7]

So what is this sequence?
Firstly we focus only upon the first word of each group. Convert it to its numeric equivalent; the interval between these numbers, as noted by Michael, is the interval between triangle numbers (To use a programmer's explanation, the interval n = n +1)

Having deduce the sequence, we convert each number into words and record its numeric length.
We then write down the two words which follow our "interval" word by increasing by 1.  We record the numeric length of those words.

Now, "With a Little Help from My Friends" ,
KS needs the number "6"

[ Extending what I believe KS had in mind the sequence beings to look like:
    4,3,5,4,3,6,8,7,7,6,9,9,11,11,10.........]

[ I'm going to claim a full solution here.  If this is not the Official Solution, then it makes a D... Good answer -  Cheers Hugo, Michael]

Posted by brianjn on 2006-02-01 04:48:37