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If you have 12 pigeons and there are only 11 roosts, then at least one roost will be quite cozy.

It was around 4 in the morning, and I'm all dressed up, ready for school, when the electricity was cut off. Too bad, I haven't put on my socks yet.

I have 2343 pairs of gray socks, 3212 pairs of pink socks and 6525 pairs of blue socks. Everything is mixed in my drawer (I'm a bit of irresponsible, sorry about that.). As there was no light, I was not able to identify the color of the socks. How many of the socks did I need to take to match one pair?

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In a box there are red and blue balls. If you select a handful of them with
eyes closed, you have to grab at least \(5\) of them to make sure at least one of
them is red and you have to grab at least \(10\) of them to make sure both colors
appear among the balls selected. How many balls are there in the box?

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