November 2016
Problem of the Month

The Hat that Didn't Sell
by Sam Loyd

Unable to sell a hat for $20, a haberdasher lowered the price to $8.
It still did not sell, so he cut the price again to $3.20, and finally to $1.28.

Assuming that he followed a system, can you predict what his next markdown will be?
You must show your work to get credit!

Solution to the Problem:

The next price would be 51 cents.

First, you must establish that each mark-down is 2/5 of the former price.
20 x = 8, so x = 8/20 or 2/5 (or 40%).
8 x = 3.20, so x = .40 or 2/5.
3.20 x = 1.28, so x = .4 or 2/5
Therefore, the next price would be 1.28 x .4 = .512 or 51 cents.

Kimberly Howe sent an excellent explanation:

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Kimberly Howe	Vienna, Virginia
3. Tom Laidlaw	Vancouver, Washington
4. Jonathan Punke	Waukegan high school, Waukegan, Illinois
5. Rosemary Walker	Mountain View High School, Mountain View, Wyoming
6. Dawson Case	Mountain View High School, Mountain View, Wyoming
7. Alyx Wells	Mountain View High School, Mountain View, Wyoming
8. Jason Stoddard	Mountain View High School, Mountain View, Wyoming
9. Ben Todd	Mountain View High School, Mountain View, Wyoming
10. Landie Bird	----------
11. Britan Woody	Mountain View High School, Mountain View, Wyoming
12. Brijesh Dave	Mumbai city, Maharashtra, India
13. stoddardt@kpmath.com	Mountain View High School, Mountain View, Wyoming
14. Kelsey Giorgis	Mountain View High School, Mountain View, Wyoming
15. Harlan Benedict	Mountain View High School, Mountain View, Wyoming
16. Adalene Thomas	Mountain View High School, Mountain View, Wyoming
17. Colton Roach	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher