Elementary POW, November 25-29, 1996
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The Emperor's Rare Coins
Remember the emperor who poured oats on the heads of his guests? Well, he has another dilemma that he needs you to solve.The emperor has nine gold coins that look exactly alike. The coins are very valuable. At a dinner party at the castle, he notices that the coins look as if they have been disturbed. All nine coins are still there but he is afraid that one of his guests has replaced one of the gold coins with a fake coin. He doesn't know what to do.
The guests are getting ready to leave and he can only stall them for a few minutes. He doesn't want to wrongfully accuse one of his guests, but he knows that if one of his precious coins is missing, his chances of recovering it will be very small once his guests leave.
The emperor knows that a fake coin will weigh slightly less than the genuine gold coins. "By the time I weigh them all, the suspects will have left," he exclaims to the empress. "Don't worry," she replies. "I can find the fake coin for you in just two weighings."
How can the empress determine which coin is fake in only 2 weighings on a balance scale?
A special thank you to Tishya, an OAC high school student who volunteered to compile this week's solutions. Tishya writes:
I am currently in grade 12 and attending Trafalgar Castle School in Ontario, Canada. My interests include music, camping, and of course, math!
Udit garg, Georgetown Day School, Washington D.C.
Teacher: Paul Nass, Grade 4
Amy Forster, grade 7; Rachel Forster, grade 3;
Huw Wilkins, grade 4, Home School
Cygnet, Tasmania,Australia.
Paul Ellebrecht, Justin Weiss, Ariel Franks,
Robbie Birge-Osborne, Brian Powers, Emily Shaw,
Nathan Strauss, and Nate Litz.
Bob Coulter's third grade math class
Forsyth School
St Louis, MO
Courtney Emerson (worked alone)
Grade: 8 Age: 13
Teacher: Donna Cleary
School: St. Elizabeth Elementary School
Location: 1500 Cedar St.
Wilm., DE 19805
Francis Chung, of Mrs. Taylor's grade 4 class
at Stoneybrook P.S.
1460 Stoneybrook Cres.,
London, Ontario, Canada
GRADE 5
C-0-H ELEMENTARY
NEW YORK
MRS. P
Kenny Aulet, grade 7, BB&N, Cambridge, MA
Math teacher Ms. Glover,
Greg , third grade, Jackson School, St. Paul
Jihad Habre, Grade 5
Mr. Kobasa
educuttr@becnet.com
York Avenue Elementary
Lansdale, PA
J.B., grade 5, Mrs. Floer's class
sstowe@int1.mhrcc.org
Cornwall on Hudson Elem., CoH, NY
Mr. Watson's math class
Turner School, West Chicago, IL. 60185
Katie Stefanis - Mr Ellsworth's 4th grade
Center School - Stow MA
Kristal Tidwell
6th grade
Murray Middle School, 921 E Inyokern Rd.
Ridgecrest, CA 93555
Ms. McMahon, teacher
bozackt@ridgecrest.ca.us
Silvije Lumani, Grade 6
Mr. Auckland's class
Locke's School
St. Thomas, Ontario
Tyler Smith, grade 4
Western Salisbury School, (Mrs. Geschel)
Allentown, PA
Miss Colwell's 6th grade class
Oak View Elementary School
Fairfax, Virginia
mcolwell@ix.netcom.com
Meghan R., Grade 5
Mrs. Crawford
Bagnall School, Groveland, MA
Student's Name: Larry Forshaw
Teacher's Name: Ellen Forshaw
School: Homeschool
5500 Millerstown Road, Urbana, OH 43078
The Emperor's Rare Coins : Solution
by Mr. Watson's math class
Turner School, West Chicago, IL. 60185What you do to solve the problem is:
- You put the coins in piles of threes.
- Take two of the piles and put one pile on each side of a scale.
- Then if they balance out you take those two piles off the scale.
- Next you take the third pile of coins and put one coin on each side of the scale.
- Then if those two coins balance the coin you didn't weigh is the odd one.
- If the coins do not balance the lighter one is the odd coin.
- If the original two piles do not balance you take the lighter pile and repeat steps numbers 4-5.
My name is Francis Chung, of Mrs. Taylor's grade 4 class at Stoneybrook P.S. (1460 Stoneybrook Cres., London, Ontario, Canada).
The following shows how to find the fake coin.
- Take the nine coins and divide them equally into three groups. Let's call these groups A, B, and C. Put groups A and B on the scale.
- If the scale is balanced, clear the scale and put two of the coins from group C on the scale (one on each side). If one of them is lighter, that is the fake coin. If the scale is balanced, the coin from group C that isn't on the scale is the fake one.
- If the scale is not balanced, take the group of three coins that are lighter, and put two coins from that group on the scale (one on each side). If one of them is lighter, that is the fake coin. If the scale is balanced, the coin from that group that isn't on the scale is the fake one.
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