Answer to April 19, 2004 Problem of the Week

Like the Fibonacci sequence 1, 1, 2, 3, 5, 8, . . . a certain turkey flock has as many turkeys on a given day as the sum of the number of turkeys on the previous two days.

If there were 79 turkeys on April 7th, and 542 turkeys on April 11th, how many turkeys were there on April 18th?

This problem is for our friends in Harrisonburg, Virginia -- the "Turkey Capital of the World."

Solution to the Problem:

There were 15,737 turkeys on the 18th.

Try to work with two unknowns, say A = the 5th number and B = the 6th number.
Then A + B = 79.
B + 79 = B + A + B = A + 2B = 8th,
2A +3B = 9th,
3A + 5B = 10th, and
5A + 8B = 11th = 542.

So solving the system {A + B = 79 , 5 A + 8 B = 542}
gives 5 A + 5 B = 395 , 3 B = 147, B = 49 , then A = 30 ;
we get 30, 49, 79, 128, 207, 335, 542, 877, 1419, 2296, 3715, 6011, 9726, 15737.

My son and my granddaughter were both born on April 18th, so I knew the answer had to be at least 2 turkeys... Just kidding, Mike and Carrie.

Larry Schwartz sent in the following: "This problem is simple if you use the Golden Ratio.
542 * phi^7 = 15737 where phi=(1+sqrt(5))/2."

I didn't think of that, and yet, every year, I assign the following program to my C++ Programming students: Find the first 20 Fibonacci numbers and write the ratio of each number to its successor. The answer approaches the number phi, which is approximately 1.618. Good thinking, Larry!

Correctly solved by:

1. Akash Patel	Columbus, Georgia
2. Jim Arrison	Norristown, Pennsylvania
3. Walt Arrison	Philadelphia, Pennsylvania
4. Richard Johnson	La Jolla, California
5. John Funk	Ventura, California
6. Chris Maggiolo	Harrisonburg, Virginia
7. Jason Storer	Winchester, Virginia
8. Alex Truong	Harrisonburg, Virginia
9. Keith Mealy	Cincinnati, Ohio
10. Franklin Harcourt	Columbus, Georgia
11. Izzy Kushner	Closter, New Jersey
12. Jeffrey Gaither	Winchester, Virginia
13. James Alarie	University of Michigan -- Flint Flint, Michigan
14. Bella Patel	Harrisonburg, Virginia
15. Helna Patel	Harrisonburg, Virginia
16. Matthew Reames	Roanoke, Virginia
17. David & Judy Dixon	Bennettsville, South Carolina
18. Mikael Wetterholm	Stocksund, Danderyd, Sweden
19. Dave Smith	Toledo, Ohio
20. Cassie Jordan	Harrisonburg, Virginia
21. Larry Schwartz	Trumbull, Connecticut
22. Kirby Welsko	Harrisonburg, Virginia
23. Megan Leach	Morris, Illinois
24. Laura LaRusso	Winchester, Virginia
25. Mark Mendez	Harrisonburg, Virginia
26. Saxton Sharad	Columbus, Georgia

April 19, 2004 Problem of the Month

Correctly solved by:

April 19, 2004
Problem of the Month