# WUSTL Putnam Practice!

## Do you like solving problems like these?  .   .   .

• Jack and Jill (two mathematicians, of course) meet at a cafe, and Jack brings up his three girls.  Jill asks him their ages. “Well”, says Jack, “the product of their ages is 36.” “Don't be ridiculous, I can't figure them out just from that!” replies Jill.  Jack looks around stealthily, and murmurs “Yeah, sorry. The sum of their ages is the number of pies in this cafe.” Jill counts the pies carefully and says, “but I still can't determine their ages!” “Ohhhh, whoops. Okay. My oldest daughter plays the piano.” How old are Jack's kids?
• Does there exist a function  f  on the xy-plane, taking only three values, such that for every pair of points p and q which are exactly one unit apart,  f(p) and f(q) are not equal?
• Find the area of the region in the xy-plane bounded by  y={1+(tan(x))2 }-1,   y=0,   x=0 and x=π/2.

### .   .   .   then you should come to the Putnam Examination practice sessions!

When: 4-6 PM Fridays, starting with an organizational meeting on Friday Sept. 16 at 4:00 PM

Where: Compton 241

Why: Learn problem solving methods and enjoy free (pizza) pies.

Who: If you have questions, please call, e-mail, or visit:
• Prof. Kerr, Cupples I Rm. 114, tel. 5-6746, matkerr@math.wustl.edu
• Prof. Bender, Compton Rm. 360, tel.5-6216, cmb@wustl.edu
• Prof. Wickerhauser, Cupples I Rm. 105a, tel. 5-6771, victor@wustl.edu
What: The William Lowell Putnam Examination is a nationwide competition in Mathematics at the level of freshman calculus.   It will be held this year on Saturday, December 3. We will also participate in the Virginia Tech Regional Mathematics Contest on Saturday, October 22.
Practice sessions are currently planned for:  Sept. 16, 23, 30; Oct. 7, 14, 21, 28;   Nov. 4, 11, 18;   and Dec. 2.   Practice problems will be posted here one week in advance of each session, except for the organizational meeting.
Practice Problems: about a week before each meeting, a list of problems to be discussed will be posted below.

Problem List 1
Problem List 2
Problem List 3
Problem List 4
Problem List 5
Problem List 6
Problem List 7
Problem List 8
Problem List 9
Problem List 10