# Lottery

iamatiger
Posers and Puzzles 30 Jan '06 20:23
1. 30 Jan '06 20:23
If you wanted to definitely win at least £10 in the uk national lottery (lotto), how many tickets would you have to buy?
2. PBE6
Bananarama
30 Jan '06 21:12
Originally posted by iamatiger
If you wanted to definitely win at least £10 in the uk national lottery (lotto), how many tickets would you have to buy?
I'm not that familiar with the UK lotto. What are the rules and the prize values?
3. 30 Jan '06 21:21
Originally posted by iamatiger
If you wanted to definitely win at least £10 in the uk national lottery (lotto), how many tickets would you have to buy?
Well you need 3 numbers and 7 balls are drawn. There are 49 balls. Those are the basic figures. There is a 1: 57 chance of winning a tenner with one ticket. I'm not sure of the best way to work out to "definitely win at least £10"
4. sonhouse
Fast and Curious
30 Jan '06 21:25
Originally posted by iamatiger
If you wanted to definitely win at least £10 in the uk national lottery (lotto), how many tickets would you have to buy?
There was a lottery in Virginia a few years ago where a company
got together and bought all the available numbers and it was
a very harrowing experience, thousands of people buying
thousands of numbers and they finally bought out all the numbers
like maybe an hour before drawing time. They definitely won but
it wasn't like ten to one or anything, MAYBE double their money
so everyone who invested made money but they said they
would never try it again, it was too chaotic and iffy, they almost
didn't buy up all the numbers in time and it turned out the winning
number was amongst the last ones bought! So if they had
just bought up, say 99% they could have lost everything and
only gotten a few thousand back. It only works if you buy
every single combination, millions of separate numbers.
5. sonhouse
Fast and Curious
30 Jan '06 21:27
Originally posted by Will Everitt
Well you need 3 numbers and 7 balls are drawn. There are 49 balls. Those are the basic figures. There is a 1: 57 chance of winning a tenner with one ticket. I'm not sure of the best way to work out to "definitely win at least £10"
So if each ticket cost one pound, then you would spend
at least 57 pounds to win ten back, or losing 47 pounds.
Such a deal....
6. 31 Jan '06 09:09
Originally posted by iamatiger
If you wanted to definitely win at least £10 in the uk national lottery (lotto), how many tickets would you have to buy?
If you really mean definitely and not only with high probability? The answer will then be - "A lot!"

But if you mean just with a probability to, let's say, 50% then it is much easy to calculate...
7. XanthosNZ
Cancerous Bus Crash
31 Jan '06 09:292 edits
Originally posted by sonhouse
There was a lottery in Virginia a few years ago where a company
got together and bought all the available numbers and it was
a very harrowing experience, thousands of people buying
thousands of numbers and they finally bought out all the numbers
like maybe an hour before drawing time. They definitely won but
it wasn't like ten to one or anything, MAY ousand back. It only works if you buy
every single combination, millions of separate numbers.
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 combinations

Originally posted by sonhouse
So if each ticket cost one pound, then you would spend
at least 57 pounds to win ten back, or losing 47 pounds.
Such a deal....

If you know the first thing about probability you know that the situation is much worse than that. Quite often you ramble on about maths or physics as if you know what you are talking about and yet this is at least the 5th time you have been completely wrong.

To be guaranteed to win at least 10 pounds (no fancy symbol here) you must have every possible combination of 3 numbers. That is 110544 combinations (49*48*47). You can pick 7 numbers per line so each line will encompass 35 combinations (7!/[3!*4!]). Therefore you need 3159 lines (rounding up obviously) to ensure you will win the prize.
8. 31 Jan '06 12:371 edit
163 tickets is require to guarantee a 3 ball win.

If anyone wants a copy of the numbers required send me you E-mail address and I'll send it through.

Ofcourse 3 balls is guaranteed plus you have way over 163 tickets that could win you other prizes........

www.bigdigitalphotography.co.uk
9. XanthosNZ
Cancerous Bus Crash
31 Jan '06 13:33
Originally posted by rlg195
163 tickets is require to guarantee a 3 ball win.

If anyone wants a copy of the numbers required send me you E-mail address and I'll send it through.

Ofcourse 3 balls is guaranteed plus you have way over 163 tickets that could win you other prizes........

www.bigdigitalphotography.co.uk
I've posted what I believe to be the correct answer in this thread already including my logic. If you are going to claim that I'm wrong at least attempt to say where. Or, if you have the list you claim to have then post it so I can find a 3 ball combination you don't account for.

10. 31 Jan '06 17:40
nice reply - why so rude ? I offered to give you the answer you wanted and all I get is a stream of abuse !

If anyone does want the list, message me on this site.

The website is just a site I'm working on - any contructive comments would be welcome if the moderator would rather I didn't have this on my posts I will remove it.
11. PBE6
Bananarama
31 Jan '06 18:51
Originally posted by XanthosNZ
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.
Your reasoning sounds correct, but I think some of the numbers are a bit off. There are 18424 combinations of 3 numbers (49 choose 3), so in order to cover all of them you would need 18424/35 = 526.4, or 527 tickets (rounding up).
12. 31 Jan '06 20:05
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 21 27
Ticket 12 : 1 6 13 15 18 25
Ticket 13 : 1 7 8 15 18 24
Ticket 14 : 1 7 13 17 22 27
Ticket 15 : 1 8 10 17 22 25
Ticket 16 : 1 13 14 21 23 24
Ticket 17 : 1 15 18 19 21 22
Ticket 18 : 1 17 19 24 25 27
Ticket 19 : 2 3 15 20 26 27
Ticket 20 : 2 4 9 12 14 27
Ticket 21 : 2 4 9 12 15 23
Ticket 22 : 2 5 11 14 16 23
Ticket 23 : 2 6 8 14 18 21
Ticket 24 : 2 6 13 17 23 25
Ticket 25 : 2 6 15 22 24 27
Ticket 26 : 2 7 8 17 23 24
Ticket 27 : 2 7 13 14 18 22
Ticket 28 : 2 7 15 21 25 27
Ticket 29 : 2 8 13 15 19 27
Ticket 30 : 2 10 15 17 18 27
Ticket 31 : 2 14 18 19 24 25
Ticket 32 : 2 17 19 21 22 23
Ticket 33 : 3 4 5 13 21 24
Ticket 34 : 3 4 5 14 15 17
Ticket 35 : 3 4 5 18 23 27
Ticket 36 : 3 4 13 16 17 26
Ticket 37 : 3 5 10 11 12 13
Ticket 38 : 3 6 7 8 20 26
Ticket 39 : 3 6 7 11 12 19
Ticket 40 : 3 6 9 16 22 24
Ticket 41 : 3 7 9 16 21 25
Ticket 42 : 3 8 9 13 16 19
Ticket 43 : 3 8 11 12 22 25
Ticket 44 : 3 9 10 16 17 18
Ticket 45 : 3 9 11 12 17 21
Ticket 46 : 3 11 12 18 20 24
Ticket 47 : 3 19 20 22 25 26
Ticket 48 : 4 5 9 13 18 20
Ticket 49 : 4 6 7 16 19 26
Ticket 50 : 4 6 9 12 19 25
Ticket 51 : 4 6 11 20 22 24
Ticket 52 : 4 7 8 9 12 22
Ticket 53 : 4 7 11 20 21 25
Ticket 54 : 4 8 11 13 19 20
Ticket 55 : 4 8 16 22 25 26
Ticket 56 : 4 10 11 17 18 20
Ticket 57 : 4 10 12 16 24 26
Ticket 58 : 4 11 16 18 21 26
Ticket 59 : 5 6 7 9 19 20
Ticket 60 : 5 6 8 11 16 25
Ticket 61 : 5 6 12 22 24 26
Ticket 62 : 5 7 11 16 19 22
Ticket 63 : 5 7 12 21 25 26
Ticket 64 : 5 8 9 20 22 25
Ticket 65 : 5 8 12 13 19 26
Ticket 66 : 5 9 10 20 21 26
Ticket 67 : 5 9 16 17 20 24
Ticket 68 : 5 10 12 17 18 26
Ticket 69 : 6 7 21 22 23 24
Ticket 70 : 6 8 10 15 21 23
Ticket 71 : 6 8 14 17 19 22
Ticket 72 : 6 10 13 14 25 27
Ticket 73 : 7 8 10 14 24 27
Ticket 74 : 7 10 13 15 22 23
Ticket 75 : 7 14 15 17 23 25
Ticket 76 : 8 13 19 21 24 25
Ticket 77 : 8 18 19 23 25 27
Ticket 78 : 9 11 13 21 24 26
Ticket 79 : 9 11 14 15 17 26
Ticket 80 : 9 11 18 23 26 27
Ticket 81 : 10 13 17 18 21 24
Ticket 82 : 10 14 19 21 22 27
Ticket 83 : 10 15 19 23 24 25
Ticket 84 : 12 13 16 20 21 24
Ticket 85 : 12 14 15 16 17 20
Ticket 86 : 12 16 18 20 23 27
Ticket 87 : 28 29 30 31 32 49
Ticket 88 : 28 29 33 38 44 47
Ticket 89 : 28 29 34 37 43 48
Ticket 90 : 28 29 35 40 42 45
Ticket 91 : 28 29 36 39 41 46
Ticket 92 : 28 30 33 37 42 46
Ticket 93 : 28 30 34 38 41 45
Ticket 94 : 28 30 35 39 44 48
Ticket 95 : 28 30 36 40 43 47
Ticket 96 : 28 31 33 40 41 48
Ticket 97 : 28 31 34 39 42 47
Ticket 98 : 28 31 35 38 43 46
Ticket 99 : 28 31 36 37 44 45
Ticket 100 : 28 32 33 39 43 45
Ticket 101 : 28 32 34 40 44 46
Ticket 102 : 28 32 35 37 41 47
Ticket 103 : 28 32 36 38 42 48
Ticket 104 : 28 33 34 35 36 49
Ticket 105 : 28 37 38 39 40 49
Ticket 106 : 28 41 42 43 44 49
Ticket 107 : 28 45 46 47 48 49
Ticket 108 : 29 30 33 34 39 40
Ticket 109 : 29 30 35 36 37 38
Ticket 110 : 29 30 41 42 47 48
Ticket 111 : 29 30 43 44 45 46
Ticket 112 : 29 31 33 36 42 43
Ticket 113 : 29 31 34 35 41 44
Ticket 114 : 29 31 37 40 46 47
Ticket 115 : 29 31 38 39 45 48
Ticket 116 : 29 32 33 35 46 48
Ticket 117 : 29 32 34 36 45 47
Ticket 118 : 29 32 37 39 42 44
Ticket 119 : 29 32 38 40 41 43
Ticket 120 : 29 33 37 41 45 49
Ticket 121 : 29 34 38 42 46 49
Ticket 122 : 29 35 39 43 47 49
Ticket 123 : 29 36 40 44 48 49
Ticket 124 : 30 31 33 35 45 47
Ticket 125 : 30 31 34 36 46 48
Ticket 126 : 30 31 37 39 41 43
Ticket 127 : 30 31 38 40 42 44
Ticket 128 : 30 32 33 36 41 44
Ticket 129 : 30 32 34 35 42 43
Ticket 130 : 30 32 37 40 45 48
Ticket 131 : 30 32 38 39 46 47
Ticket 132 : 30 33 38 43 48 49
Ticket 133 : 30 34 37 44 47 49
Ticket 134 : 30 35 40 41 46 49
Ticket 135 : 30 36 39 42 45 49
Ticket 136 : 31 32 33 34 37 38
Ticket 137 : 31 32 35 36 39 40
Ticket 138 : 31 32 41 42 45 46
Ticket 139 : 31 32 43 44 47 48
Ticket 140 : 31 33 39 44 46 49
Ticket 141 : 31 34 40 43 45 49
Ticket 142 : 31 35 37 42 48 49
Ticket 143 : 31 36 38 41 47 49
Ticket 144 : 32 33 40 42 47 49
Ticket 145 : 32 34 39 41 48 49
Ticket 146 : 32 35 38 44 45 49
Ticket 147 : 32 36 37 43 46 49
Ticket 148 : 33 34 41 43 46 47
Ticket 149 : 33 34 42 44 45 48
Ticket 150 : 33 35 37 40 43 44
Ticket 151 : 33 35 38 39 41 42
Ticket 152 : 33 36 37 39 47 48
Ticket 153 : 33 36 38 40 45 46
Ticket 154 : 34 35 37 39 45 46
Ticket 155 : 34 35 38 40 47 48
Ticket 156 : 34 36 37 40 41 42
Ticket 157 : 34 36 38 39 43 44
Ticket 158 : 35 36 41 43 45 48
Ticket 159 : 35 36 42 44 46 47
Ticket 160 : 37 38 41 44 46 48
Ticket 161 : 37 38 42 43 45 47
Ticket 162 : 39 40 41 44 45 47
Ticket 163 : 39 40 42 43 46 48
13. XanthosNZ
Cancerous Bus Crash
31 Jan '06 22:30
Originally posted by PBE6
Your reasoning sounds correct, but I think some of the numbers are a bit off. There are 18424 combinations of 3 numbers (49 choose 3), so in order to cover all of them you would need 18424/35 = 526.4, or 527 tickets (rounding up).
You are right, when calculating combinations you need to account for I forgot to divide by r!*(n-r)! (basically I forgot that order does not matter).
14. PBE6
Bananarama
01 Feb '06 07:07
Originally posted by rlg195
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
I tried a bunch of numbers with MS Excel's help, and I couldn't find any that didn't give at least a 3 number match with this list. I have to admit, it seems like a pretty clever and compact number distribution. I think it solves the problem neatly. Hey XanthosNZ, did you bust this thing or is it legit?
15. AThousandYoung