In a pack of 20 cards: blue, red, and yellow. There are six times fewer blue cards than yellow ones, and fewer red cards than yellow ones. What is the minimum number of cards you need to pull out without looking to ensure that there is at least one red card among them?

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If there is one blue card, then there are six yellow cards, and red cards: $20-1-6=13$. But then there are more red cards than yellow, which contradicts the condition.

If there are two blue cards, then there are 12 yellow cards, and red cards: $20-2-12=6$. This case satisfies the condition. Then, if you draw no more than 14 cards from the deck, they can all be blue and yellow. But if you draw 15 cards, there will definitely be at least one red card among them.

If there are no fewer than three blue cards, then there are no fewer than 18 yellow cards, which in total is no less than 21, while there are only 20 cards in total. Therefore, this case is impossible.

## Answer

15 cards.