Mistake In Close-open Cover Database?

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draughtsman
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Mistake In Close-open Cover Database?

Post by draughtsman » Sun Jan 27, 2008 7:46 am

TRANSFERED FROM OLD FORUM

Little Mistake In Close-open Cover Database

Hi Lottoarchitect,

In the section Pick 6 of close-open cover database..

Section 5 if 6 with 7 balls = 1 ticket.
It can't be 1 single ticket because 7 numbers are not compatible with a ticket of 6 numbers.


Correct wrw:
Section 5 if 6 with 7 balls = 2 tickets. (Wheel is not included in latest database version)

1 2 3 4 5 6
1 2 3 4 5 7

Well, it seems it can be done in just 1 ticket. Both Covermaster and WG indicate that C(7,6,5,6)=1 and I do not include one ticket wheels in the database. Just try it.

It is simple to understand it actually
consider the ticket
1 2 3 4 5 6

The worst case is to have a combination to test that has 6 numbers out of the 7 and the one of these to be #7 which is not in our wheel ticket, for example 2 3 4 5 6 7. If you see this combination, it still contains 5 winning numbers, so it can be done in just 1 ticket 100% 5if6. All other 6 combinations are covered as well. Wherever you found that C(7,6,5,6)=2 is a typo and if you found this wheel in Peter's site, I have already informed him some months ago for this error but he never corrected it, possibly because 2 tickets include the number 7 as well, so the wheel might be considered more balanced.

Actually, all the combinations that have to be covered are 7:
1 2 3 4 5 6
1 2 3 4 5 7
1 2 3 4 6 7
1 2 3 5 6 7
1 2 4 5 6 7
1 3 4 5 6 7
2 3 4 5 6 7
Whichever one you test, is covered by the same 1 ticket only, e.g. 1 2 3 4 5 6 covers all 7 combinations above because this ticket contains at least 5 numbers common with each of the above 7 combinations.

Hi LA,

Yes, you are right, 2 tickets are not necessary since the minimum possible for this wheel is 1 ticket,

By logic 7 numbers in 6 tickets need 2 tickets at least, but the second ticket is not necessary when we look for 5if6, so only 1 ticket is needed. Problem solve.

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