|Posted: June 8, 2007, 10:59 pm - IP Logged|
Been working a lot lately with Root Sums and formulating separate databases for combinations that Sum Total 0-10 and 21-27 separately from Sums 11-20.
Have found this useful in telling which way the combination is going to Sum Total when it doesnt Sum 11-20 which it does most of the time. Made a Root Sum database as well and have determined that the next time the digits dont Sum 11-20, the Root Sum is going to be an Even Root Sum.
In effort to figure out what this Root Sum would be I looked at the combinations that would Sum Total 21-27 and found the following:
There is no PURE Even combination that will Sum Total 21-27 except for a Doubles game. There is 1 three different digit ODD combination.
There are only 7 three different digit combinations that will Sum total 21-27 The digit 9 will be in six (6) of those combinations. The 8 will be the highest digit in the other combination.
There are twice as many Doubles combinations then there are 3 different digit combinations. There are 13 combinations in all.
Most of the Doubles combinations have either Double 8's or Double 9's. There are 4 that have Double 8's and 6 that have Double 9's.
Two combinations have Double 7's and 1 combination has Double 6's.
Out of 20 Total sets of digits 12 of the sets will have Root Sums that will be Odd. This leaves only 8 sets that will have an Even Root Sum.
Of the 8 sets that have Even Root Sums, five of the sets are Root Sum 4. Two sets have Root Sum 6 and one has a Root Sum of 8.
It appears to me that anytime you can rule out the digit 9 you can just about rule out Sums 21-27 from playing. Of the 20 different sets of digits the 9 is in 15!
AND....the 9 is only in TWO of the sets of digits that will Sum Total 0-10! 009 and 019
There is NO Root Sum 9 in Sums 21-27 except for Triple 999!
Of the 12 Odd Root Sums there are:
Root Sum 3 = six
Root Sum 5 = four
Root Sum 7 = two