Elementary POW, November 6-10, 1995
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****************************************************** Elementary Problem of the Week, November 6-10, 1995 This week's problem was submitted by Amy Barbieri, Mount St. Joseph Academy, Flourtown, Pennsylvania. Eight marbles are all the same size, shape, and color. All but one of the marbles are equal in weight. Using a balancing scale, could you find the heavy marble in only two weighings? Explain. ***************************************************** This week's Bonus Puzzler was submitted by Elissa Serrao, Mount St. Joseph Academy, Flourtown, Pennsylvania. Why can't a person's hand be 12 inches wide? ******************************************************
Hi Problem Solvers! Great job with this week's problem. Many students were able to solve the problem and find the heaviest marble but only a few could find it in only two weighings. Some of these solutions are highlighted at the end of the list. Keep up the good work! --Ruth Students who correctly solved POW 11/6-10 Katie Fleming (POW), Michael Lauritano (POW & Bonus) Mrs. Kelly's 5th Grade Class Center School Stow, MA Greg Wheeler (POW & Bonus) Miss McCarthy's 4th Grade Class Center School Stow, MA Christopher Paik (POW & Bonus) Lincoln Elementary School 3rd Grade Mrs. Nancy Kaye's Class Burlingame, CA Lynn Pat Comerford-Haley's Class Court St. School Lancaster, NY Shylah Ross (POW & Bonus) St. Mary's School Grade 5 Mr. Emmett Hoop's Class Ticonderoga, NY The Super-de-Dooper Shar-Pei's (POW) (Jenna, Jessica, and Nicholas) Linda Kubick's Class Grady A. Brown Elementary School Hillsborough, NC Elizabeth Pavlovich, Danny Mamoine, & Matt Horne (POW & Bonus) Ms. Duggan's Class 4th Grade Munsey Park Manhasset, NY Student who correctly solved the Bonus Amanda (Bonus) Mrs. Perreault's Class Wickford Elementary School 99 Phillips Street NorthKingstown , Rhode Island Jessy Krissy, Greg, Julian, Kate, Peter, Dan, Sherri & Michelle (Bonus) Jefferson Road School 5th Grade Pittsford, NY Matthew Brench, Greg Brace (Bonus) Mrs. Kelly's 5th Grade Class Center School Stow, MA Eric Winters, Brittany Rice & Rose Quinn (Bonus) Miss McCarthy's 4th Grade Class Center School Stow, MA Good Try on POW (More than 2 weighings) Michael Farrar, Erica Wysk, Katie Johnson, Greg Brace Mrs. Kelly's 5th Grade Class Center School Stow, MA Eric Winters, Brittany Rice & Rose Quinn Miss McCarthy's 4th Grade Class Center School Stow, MA Meg Perryman Minster School Michael S. Mrs. Perreault's Class Wickford Elementary School 99 Phillips Street NorthKingstown , Rhode Island Jessy Krissy, Greg, Julian, Kate, Peter, Dan, Sherri & Michelle Jefferson Road School 5th Grade Pittsford, NY
The Super-de-Dooper Shar-Pei's (POW)
(Jenna, Jessica, and Nicholas)
Linda Kubick's Class
Grady A. Brown Elementary School
Hillsborough, NC
The solution to the marble problem is:
Take 6 of the marbles and divide into 2 sets of 3 and weigh them. If these
are equal, then you will weigh the 2 remaining marbles to see which one is
heavier.
If they aren't equal, take 2 of the 3 that are heavier and weigh them by
putting one on each side. Whichever one is heavier is the heavy marble. If
these 2 are equal, the remaining marble is the heaviest.
Note: We used a balance scale to test our results.
******************************************************
Katie Fleming
Mrs. Kelly's 5th Grade Class
Center School
Stow, MA
(Katie submitted a solution which shows dividing the groups and then
branching down from each side of the scale to tell what to do with these
marbles under conditions of equality and inequality...I have summarized her
remarks in a narrative format.) 1.Marble solution: Divide marbles 3 and 3
with 2 left over. If both of these groups of three are equal, weigh the
other 2 left over marbles and the heaviest one is the one. If both of the
first groups are unequal, take the heavier group and choose 2 of the
marbles and weigh them. If these 2 marbles are equal, the one marble you
didn't weigh is the heavier one. If these 2 marbles are not equal, the
heavier one is the one you want.
******************************************************
Michael Lauritano
Mrs. Kelly's 5th Grade Class
Center School
Stow, MA
Michael Lauritano (besides the following narrative, Michael included a
drawing of the marbles and the scales which shows how he solved the
problem) 1. Yes. Divide the marbles into three groups: 2 groups of three
and
one group of two. Weigh the two groups of three on the balance scale. If
even, then weigh the other two marbles to find the heavy marble. If not
even, take the heavy group of marbles and set aside one marble. Weigh the
remaining two marbles. If they are equal, then the marble set aside is the
heavy one. If they are not equal then you found the heavy.
******************************************************
Greg Wheeler
Miss McCarthy's 4th Grade Class
Center School
Stow, MA
1. If you weigh 3 and 3 and they balance, you know it's with the
other two; so, you weigh them, and you've got it. If you weigh 3 and 3 and
they don't balance, you take the three marbles and weigh one and one. If it
doesn't balance you got it.
2. Then it would be a foot.
******************************************************
Lynn
Pat Comerford-Haley's Class
Court St. School
Lancaster, NY
Eureka ! We finally had a math wizard who solved the POW for 11/7 !
This solution comes from Lynne.
You take the 8 marbles and put 3 marbles in each side of the balancing
scale If it balances then you take the two marbles you didn't put in
the balancing scale and put them in one in each side. The side that
goes down is the side with the heavy marble in it.
If you take 3 marbles and put them in each side and they
don't balance, take 2 marbles that were in the heavy side and put 1
in each side of the balancing scale. If it balances then the 1
marble that youy didn't put in is the heavy marble.Ifit doesn't balance
the side that goes down is the heavy marble.
******************************************************
This is the answer to the problem:
First you weigh three marbles on each side. Then if one side is heavier
than the other, weigh two of the heavier side's marbles, one on each side.
Then if one side is heavier then you've found the heavier marble. If
they're the same then the one that you left out is the heavier marble. If
the three marbles on each side are the same, weigh the other two then if
one side is heavier then you've found the heavier marble.
This is the answer to the bonus promlem (rather called a joke!): If a man's
hand is 12 inches wide otherwise it would be a foot!!!
******************************************************
From:Christopher Paik,
3rd Grade
Lincoln Elementary School
Here is my solution, typed by Shylah Ross of Grade 5, St. Mary's School
Ticonderoga NY
YES, You start with 8 marbles. You take 6 and put 3 on each side of the
scale.The other 2 you keep off to the side.If the scale balences out you
simply take the 2 you marbles you kept off to the side and place them on
the scale after removing the other 6.This second will give you the heavy
marble.If the first weighing finds the heavy marble on the scale,you remove
the 3 other marbles from light end of the scale.Place 1 of the marbles from
the heavy end off to the side,and weigh the 2 remaining. If the scale
balences then the 1 off to the side is the heavy one,or the scale will show
the heavy one.
Here is my answer to the bonus puzzler:It would be a "foot!"
******************************************************
Hello, this is Elizabeth Pavlovich,Danny Mamoine and Matt Horne. We are in
Ms.Duggan's fourth grade class in Munsey Park School in Manhasset,NY.
Our answer came out to be: Put three marbles on one side of the scale and
three on the other. So you have two left over. If the two trays are evenly
balanced then none of them are the heavy marbles. Then take all of the
marbles off and put on the extras, one in one tray and one in the other. If
one of them is heavier then the other, you have found the heavy one. If one
tray is heavier than the other when you put three in, switch with your
extras one at a time.The one that makes it uneven is the heavy marble.
Bonus: Because it would be a foot.
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