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**TESTU****Banned**- Registered: 2012-06-25
- Posts: 39

Hello Everyone!

Here is a Nice little Problem "Is there a Best Any 6 Numbers from 21 From a Lotto Using the Normal 49 Balls" ?

There are Many ways to Pick Any 6 from 21 below is a Couple of Examples!

(1) Use 3 Different Any 6 from 7 Balls = Total of 21 Combinations Using 21 Balls

(2) Use 7 Groups of 3 Balls Then Pick Any 2 Groups of 3 Balls = 21 Combinations of 2 Using 21 Balls

What I am after is a Formula that Shows the Most Efficient Method!?

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,380

hi TESTU

Welcome to the forum!

And thanks for the problem. I'll leave answering it to my more skilled gambling friends.

Bob

cool avatar too!

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi TESTU

Welcome to the forum!

I don't understand your question. Could you clarify the wording a little?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**TESTU****Banned**- Registered: 2012-06-25
- Posts: 39

Hi

I am Trying to Find the Best Most Efficient way to Select Groups of 6 Balls from What May be the Best 21 Balls (Using Stats Etc.) from the 49 Balls in a Draw! Even though the 49 Balls are all the Same...Over a Period of Time All should come up at some time!

With a Maximum Selection of 21 Groups of 6 Balls (Using the Best 21 Balls) Which equals 21 Tickets at 1 Pound or 1 Euro Etc. Per Ticket.

So a Bad Selection Method would be... let's say we Chose the Numbers 4 & 12 in Every Group of 6 which would be the same Pair Chose 21 times? and the other 4 Numbers in every Group of 6 different! if possible.

The reason it's Bad is that if the Numbers 4 & 12 are not Drawn then we would lose on All 21 Tickets!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

I think I understand it now, but I dont think I can help you. I am not very good with optimisation problems, especially not with this kind.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**TESTU****Banned**- Registered: 2012-06-25
- Posts: 39

To Help Solve the Problem Below I have Laid out the Numbers Etc. Using a Grid!

So We have 21 x 6 = 126 Spaces/Boxes to fill with Our Best 21 Numbered Balls.

If we make a Grid like a Chess Board Numbered... Starting from the Bottom Left Corner Columns A - F and the Rows upwards 1 - 21

We now have Reference points which may Help to make a Formula!?

Because we want to use All the Numbers at least Once then the first Column A1 to A21 Should contain the first 21 Balls 1 to 21

This is a Good Starting Point! Now what is the Best way to fill the Other 105 Spaces/Boxes with any of our Best 21 Balls ??

Looks like this has Stumped Everyone on this Math Forum! for the Moment ?

This Below might help Someone trying to Solve this Problem!??

http://lottery.merseyworld.com/cgi-bin/lottery?days=2&Machine=Z&Ballset=0&order=1&show=1&year=-1&display=NoTables

*Last edited by TESTU (2012-06-27 02:56:01)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Hi TESTU;

Welcome to the forum. Based on stats? I need a little more and whatever data you have. A good example would be great. I can not see your grid.

(Using Stats Etc.) from the 49 Balls in a Draw! Even though the 49 Balls are all the Same...Over a Period of Time All should come up at some time!

Best balls? Lotto balls have no memory. Picking future ones based on the past is doomed.

Although biases have been discovered in Vegas wheels and in the weight of balls ( see Edward Thorpe's work ) it is now well known.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi bobbym

As I have understood it, it is like he wants to fill 21 tickets choosing 6 balls so that he has optimal chances of winning.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

That is the point. What means optimal here? All the balls have the same probability of showing up. Unless he knows something different about this lotto?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Well, if you have 21 tickets and they are all the same, there isn't a very good probability you will win.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

I do not think that is what he is after. He would not need the forum for something like that. Why is one ticket preferable to another?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

No ticket is preferable to another, but having a ticket 1,2,3,4,5,6 twice is definitely not as good as having a 1,2,3,4,5,6 and a 2,3,4,5,6,7 ticket.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

I am not sure what that means for this problem. Is he trying to avoid multiplicities?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

I think so. But I don't understand the logic by which 1,2,3,4,5,6 + 2,3,4,5,6,7 is worse 1,2,3,4,5,6 + 7,8,9,10,11,12.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Yes and until he clears up those questions progress is just a guess.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

So now we wait...

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

It is very difficult and costly to work on problems that you do not know what the OP wants exactly.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

It is.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Have not seen him around today. I will search the web for him.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**TESTU****Banned**- Registered: 2012-06-25
- Posts: 39

Quote: "I think so. But I don't understand the logic by which 1,2,3,4,5,6 + 2,3,4,5,6,7 is worse 1,2,3,4,5,6 + 7,8,9,10,11,12.

Reply All the Groups of Any 6 Numbers can be Good!? But How many times do we Repeat Each Number...

Within Any of our Best from 21 Numbered Balls! from Our Groups of 21 Combinations of 6 ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Hi;

I am not following you, please show an example of what you want. Be specific.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**TESTU****Banned**- Registered: 2012-06-25
- Posts: 39

Example Group(1) 6 Balls 1,2,3,4,5,6 Group(2) 6 Balls 1,2,3,4,5,6

Bad because Both Groups are the Same! (Unless we Win!???)

So How can we Arrange All of our 21 Groups of 6 Balls from our Best 21 Balls to Maximize the Chance of Winning!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

So you want to buy 21 tickets?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**TESTU****Banned**- Registered: 2012-06-25
- Posts: 39

Yes Buy 21 Tickets and Arrange them the Best Way to Maximize the Chances of Winning!

*Last edited by TESTU (2012-06-28 05:11:00)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

What is the payoff if you win and the price of a ticket?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**