What is the minimum number of sportlotto cards (6 out of 49) you need to buy to ensure that at least one number is guessed correctly in at least one of them?

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Let's fill eight cards as follows: in the first one, we will strike out numbers from 1 to 6, in the second one - from 7 to 12, and so on, in the last one - from 43 to 48. The number 49 will remain unstruck in any card. Therefore, at least five of the winning numbers will be struck out.

We will prove that seven cards may not be enough. Indeed, no more than 42 different numbers will be struck out in total. Therefore, at least seven numbers will not be struck out in any of the cards. It may happen that the winning numbers are exactly six of these seven.

## Answer

8 cards

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