self
Maths Puzzle
You are about to leave for holiday, but you forgot socks! You race back to your room, but all the lights are off, so you can't see the color of the socks.
Never mind, because you remember that in your drawer there are ten pairs of white socks, ten pairs of black socks, and eleven pairs of blue socks, but they are all mixed up.
How many of your socks do you need to take before you can be sure to have at last one matching pair?
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self Other Question
Years ago, to puzzle his friends, a scientist gave one of four containers containing blue and/or yellow marbles to each of the friends; Tom, Dick, Harry, and Sally.
There were 3 marbles in each container, and the number of blue marbles was different in each one. There was a piece of paper in each container telling which color marbles were in that container, but the papers had been mixed up and were ALL in the wrong containers.
He then told all of his friends to take 2 marbles out of their container, read the label, and then tell him the color of the third marble.
So Tom took two blue marbles out of his container and looked at the label. He was able to tell the color of the third marble immediately.
Dick took 1 blue marble and 1 yellow marble from his container. After looking at his label he was able to tell the color of his remaining marble.
Harry took 2 yellow marbles from his container. He looked at the label in his container, but could not tell what color the remaining marble was.
Sally, without even looking at her marbles or her label, was able to tell the scientist what color her marbles were. Can you tell what color marbles Sally had? Can you also tell what color marbles the others had, and what label was in each of their containers?
This is a famous puzzle based on the show "Let's make a deal".
The host, Monty Hall, offers you a choice of three doors. Behind one is a sports car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).
Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.
You cannot hear the goats from behind the doors, or in any way know which door has the prize.
Should you stay, or switch, or doesn't it matter?