Problem 5 (Innkeeper Problem)

After a long day hiking, three hikers stop at an inn where they order a big plate of dumplings to share between them. However, by the time the innkeeper brings the dumplings and places them on the table the hikers are sound asleep. A little later the first hiker awakes and eats one-third of the dumplings. A little later, the second hiker awakes and eats one-third of the remaining ones. Then finally, the third hiker awakes and eats one third of what is left. After that there were 8 dumplings on the plate. How many dumplings did the innkeeper prepare ?

Solution

This is one of those problems where you can start at the end and work forward. The third hiker leaves 8 dumplings on the plate, which means he found 12 dumplings on the plate and ate 4 of the 12. The second hiker left 12 dumplings, which means he found 18 dumplings on the plate and ate 6. So finally, the first hiker left 18 dumplings on the plate, which means he found 27 and ate 9. Hence, the innkeeper prepared 27 dumplings. It may be useful for you to draw a picture showing the amount each hiker eats.

[Previous]	Problem 4 (Albertsville to Bordertown Problem)
[Next]	Problem 6 (Log Problem)
[Up]	December Solutions
[Home]	Home Page
[Mail]	Send EMail to Maine Math Talent Search
[Contents]	Maine Math Talent Search Contents

Last modified on Tuesday, January 12, 1999