Puzzle One 

Help The Party Magician get ready for his show. Lost in his magic box are a whole lot of playing cards. In fact, there are 24 blue backed cards and 24 red backed cards. He need exactly two blue backed cards for his next trick. What is the smallest number of cards he needs to pull out of his box (without looking) to be absolutely sure that he has exactly two blue ones? 

Solution 
He needs to draw at least 26 cards because he could possibly draw 24 red cards in a row before drawing a blue one. 