December 2024
Problem of the Month

The Devil and Daniel Webster
Adapted from the N.C.T.M.

The devil made a proposition to Daniel Webster.
The devil proposed paying Daniel for services in the following way:

"On the first day, I will pay you $1,000 early in the morning.
At the end of the day, you must pay me a commission of $100.
At the end of the day, we will both determine your next day's salary and my commission in the following way:
I will double what you have at the end of the day (your net pay), but you must double the amount that you pay me.
Will you work for me for a month?"

How long should Daniel work for the devil?
What is Daniel's net pay (salary minus commission) after five days?
What are Daniel's total earnings (the sum of his net pays) after eight days?

The solution is:

Daniel should work for the devil for nine or ten days -- his total earnings would be $101,300.

Daniel's net pay (salary minus commission) after five days is $8,000.

Daniel's total earnings (the sum of his net pays) after eight days is $75,700.

Day #	Daniel's Salary	Commission	Net Pay	Total Earnings
1	$1,000	$100	$900	$900
2	$1,800	$200	$1,600	$2,500
3	$3,200	$400	$2,800	$5,300
4	$5,600	$800	$4,800	$10,100
5	$9,600	$1,600	$8,000	$18,100
6	$16,000	$3,200	$12,800	$30,900
7	$25,600	$6,400	$19,200	$50,100
8	$38,400	$12,800	$25,600	$75,700
9	$51,200	$25,600	$25,600	$101,300
10	$51,200	$51,200	$0	$101,300
11	$0	$102,400	-$102,400	-$1,100
:	:	:	:	:
30	-$1.02 x 1012	$5.3687 x 1010	---	---

Correctly solved by:

1. Kamal Lohia	Holy Angel School, Hisar, Haryana, India
2. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
3. Davit Banana	Istanbul, Turkey
4. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
5. Ivy Joseph	Pune, Maharashtra, India

Send any comments or questions to: David Pleacher