Elementary POW, September 30 - October 4,1996
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************************************************************ An Old Hindu Riddle Three travelers stopped at an inn for supper. The innkeeper could offer only baked potatoes. While the potatoes were baking, the travelers fell asleep. Soon, one of them woke up, saw the dish of potatoes, and took a third of them without waking the others. Later the second one woke up, saw the dish, and ate a third of the remaining potatoes. Later the third one did the same. When all three were sleeping once again, the innkeeper cleared the table and found 8 potatoes left. How many potatoes weere there to start with? Make sure you explain how you arrived at your answer. ************************************************************
Brian Powers, Nate Litz, and Nathan Strauss Forsyth School, St Louis, MO Mitchell Samson, Jamie Fierce, Grace Masters Center School, Stow, MA Julienne Bootman (bootman@value.net) Amy Forster Tasmania, Australia Greta and Bethany's groups Sea Road School, Kennebunk, Maine Elena Lobo, Udit Garg, and Vinay Aggarwal Georgetown Day School, Washington, DC Peter Moon, Eddie Kelly, David Way, Ryan Connelly, Eric Cobb, Ryan Lyle, Bryan Donahue, Rachel Victor, Autumn Tilson, Kathryn Way, and Ashley Cowart Wilder Middle School, Savannah, Georgia Julia Erdosy and Kaitlyn Missimer Mrs Chaveau's Fifth Grade (Fab Five C) Germantown Academy, Fort Washington, PA Jackie, Matthew C., Kevin, Alexander, Deidre, Joshua, Joseph, Zachary, Kurt, Matthew S., Benjamin, Andrew, Katelyn, Alexandra, Katherine, Mason, and Julie, Mrs Sandy Bennett's 3rd grade class Germantown Academy, Fort Washington, PA Katie, Lauren, Claire, Tim, and Stephen Drexel Hill School of the Holy Child, Drexel Hill, PA Christine K. Jefferson Road Elementary, Pittsford, NY Amal, Tina, Kandice, Elizabeth, Kara, Danielle, David, Heather, Lauren, Justin, Elisha, Jeff and Jeff, Ben, Mike, Stasi, Allyson, Leslie, Greg Heights Elementary Schoool, Sharon, MA J.B. Joy School in Fairbanks, Alaska Sam Harrison and Bryan Love Westwood Elementary, Westlake, LA Joey Myers and Peng Sun Hartwood Elementary, Pittsburgh, PA David LeMasters and Benjamin Stone Calvary Christian School, Sacramento, CA Branpiano@aol.com Zach Weimar School in Rose Valley, Rose Valley, PA Katie Schroeder and Margaret Timmers Blessed Sacrament School, Midland, MI Mrs Sypherd's Class Ayr School, Ayr, NE Matt Donovan and Billy Price Kerr School, Pittsburgh, PA Jordan Stormett Murray Middle School, Ridgecrest, CA Robert, sent by Nadine Dominguez-Kern Sabrina Russo Weston Salisbury School, Allentown, PA
Most innovative delivery of a solution:
Nate Litz called his solution in via cellular phone while attending a St
Louis Cardinals playoff game at Busch Stadium.
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Best explanations:
Mrs. Chauveau's Fifth Grade
We believe the answer to your problem is twenty-seven. Working backwards
helped us to solve your problem. We got the answer 27 by taking the number
8 and
finding out what eight was two thirds of, 12. Then we figured out what 12
was two thirds of, 18. Finally, we figured out what 18 was two thirds of,
27. We did it three times, one for each traveler. That's how we came up
with the answer 27. We enjoyed working out your superior problem.
****************
Kaitlyn Missimer:
3rd man: We know that 8 potatoes = 2/3 of what were on the table. So 4
potatoes = 1/3 of what he ate. So 12 potatoes were on the
table when he started to eat his 1/3 of the potatoes.
2nd man: We know that 12 potatoes = 2/3 of what were on the table. So 6
potatoes = 1/3 of what he ate. 18 potatoes were on the table when
he started to eat.
1st man: We know 18 potatoes = 2/3 of what was on the table . 9 potatoes =
1/3 of what he ate. 27 potatoes were on the table when he started
to eat.
Ans.. 27 potatoes were on the table at the start.
****************
Sudarshan K. Aggarwal:
Total Potatoes: X
The first person saw X potatoes and ate 1/3 X and left 2/3 X
The second person ate 1/3 of 2/3 X = 2/9 X so he left 2/3 X - 2/9 X=4/9 X
The third person ate 1/3 of 4/9 X, so he ate 4/27 X and he left 4/9- 4/27
which is equal to 8/27 X.
Therefore X must have been 27 if 8 potatoes were left.
I also knew that X must be a multiple of 3 so I tried 12, 18, & 27. By
this trial methos also I got 27 as the answer.
****************
David LeMasters and Benjamin Stone:
The solution they came up with is 27 potatoes. They arrived at the
answer this way: First they figured out that 2/3 times some number
equals 8. That will give you how many potatoes were there when the
last traveler ate. The answer to that is 12. Then you repeat the
same process (2/3 times some number equals but now instead of 8, you
use 12). That answer is 18, which gives you the amount of potatoes that
were there when the second traveler started to eat. You repeat the process
one more time using 18 now instead of 12, and arrive at the final answer of
27.
****************
Zach Weimar:
I think there were 27 potatoes.
I looked at how many were left: 8. If the third man ate one-third then
two-thirds are left. If you split 8 into two parts you get 4. That means
he ate 4.
I added the 4 he ate to the 8 left and got 12.
This is how many were left by the second man. He ate one-third and left
two-thirds. Split 12 into two parts and you get 6. So he ate 6.
I added the 6 he ate to the 12 left and got 18.
This is how many were left by the first man. He ate one-third and left
two-thirds. Split 18 into two parts and you get 9. So he ate 9.
I added 9 to the 18 he left and got 27.
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