Department of Mathematics and Statistics


Department of Mathematics

Putnam Exam

Problem of the Month

Fall 2015

Problem 2, October 2015

Three men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognizes the three as friends and asks the waiter to return $5 to the men.

The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.

Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14.....where has the other $1 gone from the original $15?
(solution due before November 1st 2015)

Problem 1, August 2015

A cake has a quadrilateral shape (four sides). We cut the cake along the two diagonals and eat one of the four pieces. The three remaining pieces weight: 120 grams, 200 grams and 300 grams respectively. What was the initial weight of the cake? (solution due before September 15th 2015).

Please submit your solution for this month problem no later than 1-st of the next month. Try to keep your solution to less than two pages. My office is in MSC 426 and my email address is You may also put your solution in my mailbox (Mihai Staic).

If you want to propose a problem please contact me by email or in person.