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In Lotto (the UK lottery), you pick 6 numbers from a pool of 49. How many tickets would you need to guarantee at least one match of 3 numbers?

Wikipedia shows the probability of matching 3 numbers at 55:1. Does that mean if you buy 55 tickets you are guaranteed to get at least one match?

(P.S. I did search here and find another lottery question, possibly asking the same thing - but obviously didn't understand that.)

cheers

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Should we add the [combinatorics] tag? –  cardinal Sep 21 '11 at 23:39
    
@cardinal: At least that would be more appropriate than probability, since the question does not involve any probabilities. –  TMM Sep 22 '11 at 0:20

1 Answer 1

up vote 6 down vote accepted

Believe it or not, this is an open problem. Up to the present time, despite advanced mathematics and supercomputers, the precise minimum is unknown. It is known that the minimum value (called $L(49,6,6,3)$ in mathematical terminology) lies between $87$ and $163$. There is more information on this topic here.

Here is a set of $163$ ticket choices that works. Maybe a smaller set could be found to guarantee 3 winning numbers, but nobody knows this for sure.

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It seems a bit over my head, but thanks for the answer. –  smeghead Sep 22 '11 at 0:14
    
You're welcome! –  Byron Schmuland Sep 22 '11 at 0:33

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