Answer to March 31, 2003 Problem of the Week

On a recent trip to Ohio, my wife and I stopped at a Drive-In restaurant called Swensons.

The Menu advertised 17 flavors of milkshakes which were available in two sizes.

For an additional 15 cents, you could combine any two flavors.

How many different milkshakes does Swensons serve?
Consider a regular chocolate shake different from a small chocolate shake.

Solution to the Problem:

The answer is 306 milkshakes.

Bob Hearn sent in the following answer:

First, there are 17 different one-flavor milkshakes, but they can be ordered in two different sizes.

This gives 34 different one-flavor shakes.

To determine the number of two-flavor milkshakes, take the combination of 17 flavors taken two at a time.

This yields 136 but again they can be ordered in two different sizes.

Hence, there are 272 different two-flavor shakes which can be ordered.
So the total number of different milkshakes which Swensons makes is 34 + 272 = 306 !!!

Correctly solved by:

1. Walt Arrison	Philadelphia, Pennsylvania
2. Mr. and Mrs. William Funk	San Antonio, Texas
3. David & Judy Dixon	Bennettsville, South Carolina
4. Rick Jones	Kennett Square, Pennsylvania
5. Wayne Price	Beatrice, Nebraska
6. Matt Stillwagon	Winchester, Virginia
7. Richard Johnson	La Jolla, California
8. Bobby Martin	Columbus, Georgia
9. James Alarie	University of Michigan -- Flint Flint, Michigan
10. Tina Zahel	Winchester, Virginia
11. Keith Mealy	Cincinnati, Ohio
12. Bob Hearn	Winchester, Virginia
13. Ben Reames	Columbus, Georgia
14. Ashley Neumann	Winchester, Virginia
15. Pam Coffield	Columbus, Georgia
16. Jeffrey Gaither	Winchester, Virginia
17. Michael Rodriguez	Great Falls, Montana

March 31, 2003 Problem of the Month

Correctly solved by:

March 31, 2003
Problem of the Month