Answer to March 31, 2003 Problem

Swensons Milkshake Problem

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 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