I'm still curious what the circumstances are that are making this pattern
necessary for Ken... if you don't mind sharing, Ken. ;o)

I have no knowledge of why Ken needs the pattern, but it is a classic pattern 
for improving the odds of winning lotteries and similar entities.  The idea is 
that you pick a series of numbers and the find all the possible permutations of 
winning combination subsets in that series of numbers.  Then buy tickets for 
all these combinations.  Thus if any winning combination of your numbers are 
drawn you are guaranteed to posses that winning ticket.  How many numbers you 
choose and how long of a winning combination you want determines how many 
tickets you need to buy to cover all the possibilities.

A basic sample would be that you pick the nine numbers 1,2,3,4,5,6,8,9.  You 
then find all the possible permutations of 3 numbers in that list (The minimum 
winning combination in many lotteries).  You then buy tickets that contain all 
those combinations.  Then if any three of your nine numbers are drawn you are 
guaranteed to have at least one winning ticket. 


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