You have nine pearls, eight are real and one is fake. All the real ones weigh the same, but the fake weighs less than the real ones. Using a balance scale, how can you determine which one is the fake? The best solution (the one that’s published) will be the one that uses the scale the fewest times. |
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Solution by: Sarah Brooks, Berkley High School
Step 1: Separate the pearls into three groups of three.
Step 2: Place two of the groups on each side of the balance scale. If they weigh
the same, then the fake is in the group that is not on the balance scale. If
one of the groups on the scale weighs less, the fake is in that group.
Step 3: Take the group containing the fake, and put one pearl on each side of
the balance scale. If the two pearls weigh the same, the fake is the one that’s
not on the scale. If one weighs less than the other, then that is the fake.
Other students whose solutions used the scale twice:
David Krueger, Will Quinn, Kyle Safran (Grosse Pointe South H.S.); Martha Pelieg
(Rockford H.S.); Alexandra Collins-Webb, Armila Francis, Sharon Frank, Megan
Greve, Patrick Lutz, Paula Manni, Sarah Roth, Lauren Valentine, Bethany Welton
(Plymouth Christian Academy); Steve Drassoo (East Lansing H.S.); Morgan Bissell,
Brooke Boer, Adam Booth, Allison Bryan, Max Dixon, Mischa Dylewski, Andrew Engle,
Rebecca Hammond, Nate Hopkins, Scott Howard,Haley Kammeraad, Merideth Loree,
Christy Maier, Alex Piskin, Hillary Piskin, Drew Reyelts, Andrew Rennaker, Brandon
Schabes, Kailene Schabes, Kylie Shuneson, Caroline Sierra, Gina Turner, Dani
Tyner, Niki Tyner, Doug Waldo (Forest Hills Eastern H.S.); Tori Dober (Dundee
H.S.); Erica Wozniak (Marquette Sr. H.S.); Shou-Hsuan Liu, Pulkit Monga, Gavin
Patient (Novi H.S.); Chad Smoyer (Hanover-Horton H.S.); Thao Dinh (Holland H.S.);
David Maniez (St. Louis H.S.); Johnathon Baker (Bullock Creek H.S.); Willa Chen,
Yu Han (Plymouth-Canton Educational Park); Carolyn Affholter, Sarah Fowler,
Danny Hamilton, Kristen VanNoord (Forest Hills Northern H.S.); Max Hirschhorn
(West Bloomfield H.S.); Chelsea Fogwell, Robert Harrison, Hannon Maylee, Chantelle
Pline, Alex Robinson (Lansing Catholic Central H.S.); Joe Fetterhoff, Audrey
Glubzinski, Karrie Juengel, Erik Larson, Eric Whitaker, Joe Wright (Linden H.S.);
Nikhil Chavali, Eric Morris, Uday Sarvepalli, Jack She (Saginaw Heritage H.S.);
Shawna Wei, Jay Yang (Forest Hills Central H.S.); Justin Travis, Kelsey Travis
(Shepherd H.S.); Karl Crist, Ryan Klock (No school given)
Students whose solutions could require more than 2 uses of the scale:
Benjamin Blanchard, Anisha Chadha, Meng Meng Jie, Scott Kelber, Gregory Korma,
Ryan Pollard, Camille Press, Duggan Quinn, Roland Razburgaj (Novi H.S.); Allison
Assaly, David Bliss, Clare Boals, Bill Darden, Michelle DeWitt, Melvin Joice,
Sonya Kavalam, Kristin Kopec, Laura Portko, Joe Sugiyama, Marc Walker (Forest
Hills Eastern H.S.); Dan Dou, Lars Hamre (Grosse Pointe South H.S.); Sarah Hallinen,
Akhilesh Menawat, Maha Siddiqui, Nick Wasylyshyn (Canton H.S.); Joseph Cluley,
Heather Davis, Sheila Saurman (St. Louis H.S.); Nicholas Tanner (Benzie Central
H.S.); Jessica Holberg, Mark Thayer (Lansing Catholic Central H.S.); Amir Abidov
(West Bloomfield H.S.); Meghan Calloway, Whitney Herman, Stephanie Malburg,
Michelle McMahon, Maurice Wong (Forest Hills Northern H.S.); Sarah Altken, LeeAnne
Carr, Jessica Greenfield, Cameron Groenewoud (Plymouth Christian Academy); Zack
Smith (Salem H.S.); Michael Gustin (Bullock Creek H.S.); Tyler Bradley, Josh
Eschtruth, Hanna Espie, Brittanie Pruitt, Megan Schinderle, Lauren Stevenson,
Jared VanderMoere, Jennifer Wickham (Grand Ledge H.S.); Bobby Carsey, Grace
Conley, Kaylen Dickerson, Alisha Kohler, Theresa Laubrick, Dan Porter, Kelly
Tomasek (Linden H.S.); Chelsea Nayback (Petoskey H.S.); Tom Angers, Jimmy Galus,
Ben Modlin, Kim Scioli, Gabe Solo, Jacob Webster, Jessica Westphal (Saginaw
Heritage H.S.); Andrew Brecht, Kaitlyn Brock, Morgan Brown, Alissa Coldwell,
James Custer, Jordan DeLong, Anna Hickey, Derek Jessup, Ashley Meyer, Kyle Recker,
Josh Shafer, Sheila Wheeler, Hannah Wilcox (Shepherd H.S.); Pranav Moudgil (Detroit
Country Day H.S.); Lauren Bacans (No school given)