Math 160 Mathematical Problems and Games, Fall 2002
Problem Set 1:  hand in one problem Tuesday, Sept. 10.

Think about all four problems, and come up with some ideas about how to solve them.  
Then choose one of the problems and write up a careful solution.   Your solution should be 
written so that it would convince a skeptical classmate.

1.  In a certain year, there were four Fridays and four Mondays in January.  What day of 
the week was January 17th that year?

2.  Suppose you have a mug of milk and a mug of tea.  You take three tablespoons of milk 
and put it in the tea, and stir it well.  Then you take three tablespoons of the mixed milk and 
tea and put it back into the milk.  Which is greater, the percentage of milk in the tea or the 
percentage of tea in the milk?  Or are they equal?

3.  You have two egg timers (the kind with sand in an hourglass), one that measures seven 
minutes and one that measures eleven minutes.   You want to boil an egg for exactly 15 
minutes.  How can you time it using these two timers?

4.  You have seven glasses on a table, all face down.  You are allowed to turn over four 
glasses at a time, as many times as you want.  Is it possible to end up with all seven glasses 
face up?