Lottery Ticket ................
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Lottery Ticket ................
The lottery (in the UK) consists of 6 balls being drawn out of a total of 49 (numbered 149) .... plus another ball is drawn out of the remaining balls  this is the "bonus ball", but is irrelevant to this question.
When you purchase a lottery ticket, you pick 6 different numbers in the range 149.
If you have 3 numbers, you win £25. ..... obviously more numbers = a bigger win.
My question is, what is the minimum number of lottery tickets that I would have to buy, to guarantee that I win at least £25 ??
Now according to: http://lottery.merseyworld.com/Info/Chances.html
..... the odds of getting 3 numbers are approx 1 in 57 .... but if you buy 57 tickets, you're not guaranteed a win.
Permutations and combinations, etc, is not my strong point ...... anyone any ideas please ??
When you purchase a lottery ticket, you pick 6 different numbers in the range 149.
If you have 3 numbers, you win £25. ..... obviously more numbers = a bigger win.
My question is, what is the minimum number of lottery tickets that I would have to buy, to guarantee that I win at least £25 ??
Now according to: http://lottery.merseyworld.com/Info/Chances.html
..... the odds of getting 3 numbers are approx 1 in 57 .... but if you buy 57 tickets, you're not guaranteed a win.
Permutations and combinations, etc, is not my strong point ...... anyone any ideas please ??
 Lopsidation
 Posts: 183
 Joined: Tue Oct 27, 2009 11:29 pm UTC
Re: Lottery Ticket ................
Not an answer, but deserves a spoiler anyway:
Let's get the ball rolling. I can do it in 875 tickets. That sucks, though. I bet picking a few hundred random tickets would work, even without a clever strategy.
Spoiler:

 Posts: 43
 Joined: Fri Sep 02, 2011 11:20 am UTC
 Location: CT, USA
Re: Lottery Ticket ................
I think the upper bound is:
Spoiler:
Re: Lottery Ticket ................
nicklikesfire wrote:I think the upper bound is:Spoiler:
i think you're confusing the way tickets are picked in this game for a different game. You're not picking a number between 1 and 100000, you're picking six numbers between 1 and 49.
A true upper bound is
Spoiler:
You're on the right track though, because
Spoiler:
edit:
here's my solution track so far
Spoiler:
Re: Lottery Ticket ................
Xias wrote:A true upper bound isSpoiler:
I'm not sure that really is a proven upper bound.
Spoiler:
 Lopsidation
 Posts: 183
 Joined: Tue Oct 27, 2009 11:29 pm UTC
Re: Lottery Ticket ................
Maybe some kind of Pigeonhole argument will help?
Spoiler:
Re: Lottery Ticket ................
Apparently it's called The UK National Lottery Wheeling Challenge and the record, so far, for the minimum number of tickets guaranteed to match 3 numbers is:
and a list of all the tickets, can be found here
Now according to:
http://math.stackexchange.com/questions ... oguarante
.... the true value is reckoned to be between ... although, as of yet, no one has got lower than the upper limit ....
Spoiler:
and a list of all the tickets, can be found here
Now according to:
http://math.stackexchange.com/questions ... oguarante
.... the true value is reckoned to be between
Spoiler:
Re: Lottery Ticket ................
Moonbeam wrote:.... the true value is reckoned to be between... although, as of yet, no one has got lower than the upper limit ....Spoiler:
Of course not. If someone did, that would be the new upper limit.
addams wrote:This forum has some very well educated people typing away in loops with Sourmilk. He is a lucky Sourmilk.
 Moose Anus
 Posts: 420
 Joined: Fri Oct 14, 2011 10:12 pm UTC
Re: Lottery Ticket ................
It seems like you could cut out a few of the numbers from the wheel.
Spoiler:
Lemonade? ...Aww, ok.

 Posts: 6
 Joined: Sun Nov 30, 2008 5:55 am UTC
Re: Lottery Ticket ................
Is it just me, or should the bounds be much higher?
Spoiler:
Re: Lottery Ticket ................
ToastOfDestiny wrote:Is it just me, or should the bounds be much higher?Spoiler:
I think it's like this:
Spoiler:
 ThirdParty
 Posts: 347
 Joined: Wed Sep 19, 2012 3:53 pm UTC
 Location: USA
Re: Lottery Ticket
Since, aside from Moonbeam's links, nobody's said anything about a lower bound yet, here's a simple proof that we need at least 54 tickets:
Spoiler:
Re: Lottery Ticket
ThirdParty wrote:Since, aside from Moonbeam's links, nobody's said anything about a lower bound yet, here's a simple proof that we need at least 54 tickets:Spoiler:
That was what I was trying to calculate above, and I see that my mistake was that for some reason I divided by 6*5*4 instead of 6!. That explains why my lower bound was so much higher than proven upper bounds. So, thanks for showing me my error (even though you seem to have missed my post entirely, judging by your first sentence ).
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