Originally posted by XanthosNZI don't think it is though. I recall watching a programme about it a few years ago, although whether it was the Virginian lottery or another does escape me.
With 49 numbers from which 7 are drawn* there are 8.59 million combinations. Your story sounds like a load of crap.
It had rolled over several times, so the prize money on offer was much bigger than the amout to be spent on tickets. Sending people around the state to buy them, thanks to some vendors refusing to sell as many as they wanted the group weren't able to buy all the tickets (only about 90% or something), but did win and make some money.
Of course it would have been foiled with too many people sharing the prize too.
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2 edits
Originally posted by XanthosNZThe flaw with this is as follows:
With 49 numbers from which 7 are drawn* there are 8.59 million combinations. Your story sounds like a load of crap.
*I'm taking the numbers from Will's definition of the UK lotto but the Virginia lotto may be different, for example in NZ the lotto is 6 numbers from 40 (a bonus ball which counts for lower divisions is included) which is 3.83 million com ...[text shortened]... *4!]). Therefore you need 3159 lines (rounding up obviously) to ensure you will win the prize.
You don't need every possible combination, you need one of the combinations you have got to be on every ticket.
Consider ways of selecting 3 items from 6, there are 20 of these as follows:
abc
abd
abe
abf
acd
ace
acf
ade
adf
aef
bcd
bce
bcf
bde
bdf
bef
cde
cdf
cef
def
Say you are trying to buy as few 3-letter tickets as possible to ensure that whatever combo comes up you have 2 letters right.
if you buy the combo abc, you have covered all tickets with a&b, a&c or b&c
This leaves
ade
adf
bde
bdf
bef
cde
cdf
cef
def
Which can all be covered by buying the combo def
So, there are 15 two letter combinations possible, and each ticket covers 3 of them, why did we need only two tickets and not 5?
well - look at the combinations we missed out, they are:
ad
ae
af
bd
be
bf
cd
ce
cf
We have ensured that if a card comes up with two of these combinations on it, they will combine to give us a third combination that we have covered!
The ideal "cover" for a given lottery depends on finding a the smallest set of tickets with this property of covering every combination of the uncovered combos. It is not a simple matter of probability.
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Originally posted by rlg195Nice one! I guess you found this somewhare like:
163 lines ;
Ticket 1 : 1 2 3 4 5 10
Ticket 2 : 1 2 9 10 11 26
Ticket 3 : 1 2 9 10 14 23
Ticket 4 : 1 2 10 12 16 20
Ticket 5 : 1 3 14 20 23 26
Ticket 6 : 1 4 9 12 15 27
Ticket 7 : 1 4 12 14 18 23
Ticket 8 : 1 5 11 14 16 27
Ticket 9 : 1 5 11 15 16 23
Ticket 10 : 1 6 7 10 18 19
Ticket 11 : 1 6 8 17 2 ...[text shortened]...
Ticket 161 : 37 38 42 43 45 47
Ticket 162 : 39 40 41 44 45 47
Ticket 163 : 39 40 42 43 46 48
lottery.merseyworld.com/Wheel/Wheel.html