Lotto Combinations Question

Hi, Can someone please help me with this:

In my local lotto game, six numbers are drawn from 45 numbers. I know the odds of getting 3 numbers correct are 45-1. Is there a way to play 45 tickets to guarantee that one or more will have 3 correct numbers? I'm trying to find an example of the 45 combinations of 6 numbers I could play that would guarantee this.

TIA

If I understand the question correctly, then I would calculate like this

We know that the probability of guessing three numbers = 0,022441. Then using the binomial distribution, we can calculate the probability of how many tickets 3 numbers will guess, if we by buying 45 tickets with different numbers:
0 = 0.36012
1 = 0.37200
2 = 0.18786
3 = 0.06181
4 = 0.01489
5 = 0.00280

Then we get, with a probability 63,9% among 45 tickets you will have from 1 to 5 tickets with three guessed numbers

Thank you for your response! Much appreciated!

Quote: Edpokernut

Hi, Can someone please help me with this:

In my local lotto game, six numbers are drawn from 45 numbers. I know the odds of getting 3 numbers correct are 45-1. Is there a way to play 45 tickets to guarantee that one or more will have 3 correct numbers? I'm trying to find an example of the 45 combinations of 6 numbers I could play that would guarantee this.

TIA
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This is a well-known problem (that is, "What is the minimum number of tickets in order to guarantee that at least one will have 3 numbers, if 6 numbers are drawn from N, for some N?"). Unfortunately, there is no easy solution. However, I don't think 45 tickets would be enough.

For a 6/49 lottery, like the one in the UK, the smallest number of tickets so far that anyone has found is 163.

At least I know for my 6/45 lotto it would be less than 163. My friend telling me that guaranteeing one number is playing just 8 tickets, (duh) so it shouldn't be hard to figure out 3, HAHA. I looked up that link and found some good information. Thank you.