Originally posted by jimslyp69
A chauffer has 5 pairs of white gloves, 3 pairs of black gloves and 2 pairs of brown gloves in his draw. Without looking, how many gloves does he need to pull out of the draw to be sure he makes a complete pair?
ANd another one...
How many cards can be pulled out of a complete set of 52 playing cards, without having a full house combination?
(1) The chauffeur can pull out 5 lefty white gloves, 3 lefty black gloves and 2 lefty brown gloves. After that, the next glove will complete some pair, so the chauffer needs to pull out 5+3+2+1 = 11 gloves to be sure.
(2) A full house, consisting of one pair and one three of a kind, can be put off the longest by drawing a pair from each rank. After that, any card will complete some three of a kind making a full house. So the most cards that can be drawn without making a full house is 13*2 = 26 cards. The 27th card will make the full house.
Interesting questions. These are examples of problems that can be solved using the pigeonhole principle, a simple but powerful mathematical tool.