Math 1050 Section 1 Puzzle 1
Name:
One hundred people stand in a strait line all facing one direction. An overseer
comes by and places a yellow or pink hat on each person in the line. Starting from
the back of the line (person that can see everybody in front of them) each person
will call out a color either yellow or pink (you can assume that everybody can see
the color of all the hats of the people in front of them in the line). If the color they
call out matches the color of the hat on their head then each person in the line gets
1 million dollars. Thus if 5 people get the correct hat color then all 100 participants
get 5 million dollars. The people in the line however know what is going to happen so
the night before they got together and developed a strategy to maximize the amount
of money everybody would be guaranteed .
1. Can you nd a strategy where each person is guaranteed 1 million dollars?
2. How about 50 million?
3. Is it possible to guarantee more?
To get credit for the problem write the best strategy you can come up with on the
back of this piece of paper and turn it in before or on the 17th of January for credit.
You need to explain the strategy fully to get credit. Good Luck!!!!