Answer to Problem of the Month for February 2007

In the comic strip below, how many hours of homework will she have to do in 36 weeks?

COMIC STRIP is no longer available.

Solution to the Problem:

She would do 68,719,476,735 seconds of homework or 19,088,743 hours!!!!
However, it would be physically impossible to fulfill the contract. The number of seconds in a week is given by 7 x 24 x 60 x 60 = 604,800 seconds.
On the 20^th week, she would have to do 2¹⁹ or 524,288 seconds of homework.
On the 21^st week, she would have to do 2²⁰ or 1,048,576 seconds of homework, which is more than the number of seconds in a week!

So, the real answer would be 10,725,375 seconds or 178,756.25 minutes or 2,979 hours of homework.
For the first 20 weeks, she would do 1,048,575 seconds of homework. Then the best she could do after that would be 604,800 seconds per week for the remaining 16 weeks as long as she doesn't sleep or eat or go to school.

To see this pattern, try a table:

Week #	Seconds of Homework that Week	Total Seconds of Homework
1	1 = 2⁰	1 = 2¹ - 1
2	2 = 2¹	3 = 2² - 1
3	4 = 2²	7 = 2³ - 1
4	8 = 2³	15 = 2⁴ - 1
...	...	...
20	524,288 = 2¹⁹	1,048,575 = 2²⁰ - 1
21	1,048,576 = 2²⁰ Not possible!	2,097,151 = 2²¹ - 1
...	...	...
36	= 34,359,738,368 = 2³⁵	68,719,476,735 = 2³⁶ - 1

David and Judy Dixon were the first to note that she would not be able to keep up with her homework by the 21st week.

Correctly solved by:

1. James Alarie	University of Michigan -- Flint Flint, Michigan
2. Sagar Patel	Brookstone School Columbus, Georgia
3. David & Judy Dixon	Bennettsville, South Carolina
4. Shaan Arora	Brookstone School Columbus, Georgia
5. Richard K. Johnson	La Jolla, California
6. John Funk	Ventura, California
7. Tristan Collins	Virginia Tech Blacksburg, Virginia
8. Mr. Robb's Discrete Math Class	John Handley High School Winchester, Virginia
9. Neal Amos	Brookstone School Columbus, Georgia

February 2007 Problem of the Month

Correctly solved by:

February 2007
Problem of the Month