Elementary POW, February 19-23, 1996
Elementary POW Problems || January-March, 1996 Problems || Elementary POW Main Page
****************************************************** Elementary Problem of the Week, February 19-23,1996 This week's problem was submitted by Debbie Goddard, Grade 10, Mount St. Joseph Academy, Flourtown, PA. You have two empty jugs. One will hold 5 gallons of liquid, the other will hold 3 gallons of liquid. Each jug has a line at the top showing exactly where the 5 gallon or 3 gallon mark is. Here is the problem. You need exactly 4 gallons of water. You have nothing available to you other than the jugs and a pool of water. An estimate won't do. It has to be exactly 4 gallons. You can empty or fill the jugs as many times as necessary, or pour the contents of one jug into the other. How would you accomplish this? ***************************************************** Bonus Puzzler A "perfect" number is a number whose factors other than the number itself when added together equal that number. For example, 12 is not a perfect number because its factors, other than itself are 1, 2, 3, 4, and 6 and 1+2+3+4+6 does not equal 12. There are two perfect numbers that are less than 30. Can you find them and show that they are perfect? ******************************************************
****************************** Zachary Sandler Paul's 4th grade math Georgetown Day School Washington, DC, ****************************** Jaclyn Cohen Fifth grade Paul Nass Georgetown Day School Washington, DC. ****************************** Matt Rogan. Washington D.C. Georgetown Day School. Paul Nass Fourth Grade *********************************** Byron Armstrong and Collin Willis 4th grade Paul Nass Georgetown Day School *********************************** Sydney Selzer 5th Grade Paul Nass Georgetown Day School Washington D.C. ************************************ Benjie Achtenberg, Jonathan Magaziner, Will Urquhart, Richard Minkoff Paul Nass Fifth grade Georgetown Day School Washington, D.C. ************************************** Mike Grade 4 Paul Nass Georgetown Day School Washington D.C ***************************************** David M. Driscoll Joan's 4th Grade Georgetowm Day School Washington D.C. ******************************************* Annie Bolotin Joan's 4th grade Georgetown Day School Washington D.C. ******************************************* Kate Forscey Fourth Grade Paul Nass Georgetown Day School Washingon, D.C. ******************************************** Paul Nass Georgetown Day School Washington, D.C. ********************************************* Anna Margush Grade 4 Home School Akron, Ohio ********************************************* Simone Levien 4th grade Paul's math class Georgetown Day School Washington D.C. ******************************************* Sam Langer Georgetown Day School Washington, DC Teacher: Paul Nass Grade: 5th ******************************************* Brad Jadlowiec ****************************************** BRIAN T KING 5TH GRADE ******************************************* Ryan Grace, Kim Fugok, Christine McGowan, and Amanda Tumminelli Grade 6 Mrs. Brennan Drexel Hill School of the Holy Child Drexel Hill, PA ******************************************* Tommy Grace 5th Grade Paul Nass Georgetown Day School Washington D.C. ******************************************** Phillip Grade 4 Mandarin Oaks Elementary Jacksonville, FL ********************************************* Todd Feiler, Matt Spindler, Evan Mossman 4th grade Fred Rimmel Kerr Elementary Pittsburgh, PA ********************************************* Meghan Ramsey Grade 4 Miss Seager Bagnall School ********************************************* Meghan Lovett Gr. 4 Ms. Seager Bagnall School ******************************************** Grade: 4th Problem of the Week School: Georgetown Day School Student's Name: Luis Mendoza Teacher: Paul Nass ********************************************* Brittany Kress Grade 5 Miss Planz Marzoff Elementary School Pittsburgh, PA ************************************************* Aneil Baron Paul Nass Georgetown Day School Washington,DC 3rd grade *************************************************** Mitchell Malasky Grade 4 Joan Foster Georgetown Day School Washington D.C. *********************************************** Laura Fraser Ms. McCarthy 5th grade class Center School ************************************************ Kristin Squires Mrs. Pensa Third grade Center School Stow, Ma ************************************************** Sam Hahn Ms. McCarthy 4th grade Center School Stow, MA ************************************************** Ted Powers Mrs. Pensa 3rd grade Center School Stow, MA ************************************************** Sam DeLuca Mr. Ellsworth 4th grade Center School Stow MA
25 answers were correct from the 32 that were sent in. We even recieved a
response from Australia!! Congratulations to everyone.
************************
My name is Zachary Sandler. I am in Paul's 4th grade math
group. I go to Georgetown Day School in Washington, DC, on MacArthur
Blvd.. Here is my answer:
Fill up the 5 gallon jug with water. Fill up the 3 gallon jug with the
water from the 5 gallon jug. Pour the 3 gallon jug out. Pour the 2
gallons of water left in the 5 gallon jug into the 3 gallon jug. Fill up
the 5 gallon jug from the pool. Fill up the 3 gallon jug with one gallon
of the water in the 5 gallon jug. Pour out the 3 gallon jug. Now the 5
gallon jug has 4 gallons of water in it.
***************************************************************
Jaclyn Cohen. I am in the fifth grade. My teacher's name is Paul
Nass. I go to Georgetown Day School in Washington, DC.
Problem of the week February 19-23.
My answer is:
1) You pour 5 gallons into the 5 gallon jug from the pool of water
2) Pour 3 gallons into the 3 gallon jug from the 5 gallon jug
3) Now you have 2 gallons in the 5 gallon jug and 3 gallons in the 3 gallon
jug
4) Pour the 3 gallons out from the 3 gallon jug
5) Now you have 2 gallons in the 5 gallon jug and 0 in the 3 gallon jug
6) Pour 2 gallons into the 3 gallon jug from the 5 gallon jug
7) Pour 5 gallons into the 5 gallon jug from the pool of water
8) Pour 1 gallon into the 3 gallon jug from the 5 gallon jug
9) Dump out the 3 gallons from the 3 gallon jug
10) NOW YOU HAVE 4 GALLONS IN THE 5 GALLON JUG!!!!!!
*****************************************************************
Matt Rogan. Washington D.C. Georgetown Day School. My teacher is Paul
Nass. Fourth Grade
Fill five gallon jug. Pour three gallons into three gallon jug. Empty three
gallon jug. Pour two gallons left in five gallon jug into three gallon jug.
Fill five gallon jug. Pour as much of five gallon jug into three gallon jug.
Empty three gallon jug. You have four gallons left in five gallon jug.
*******************************************************************
Byron Armstrong and Collin Willis
4th grade Paul Nass Georgetown day school
Fill the three gallon jug pour it in the five gallon jug fill the three
gallon jug again pour in five as much as you can then dump the five gallon
jug pour the one gallon from the three gallon jug then fill the three and
pour in five and you have four gallons
********************************************************************
Sydney Selzer, 5th, Paul Nass, Georgetown Day School, Washington D.C.
First fill up the 3 gallon and pour it into the 5 gallon jar. Do it again
and you should have 1 gallon left. Then empty the 5 gallon and pour the one
gallon into the 5 gallon jar. Fill the 3 gallon jar and pour it into the 5
gallon jar and you have 4 gallons!
********************************************************************
Benjie Achtenberg, Jonathan Magaziner, Will Urquhart, Richard Minkoff.
Paul Nass is our math teacher, fifth grade, Georgetown Day School, Washington
D.C.
Take the five gallon container and fill it. Then you dump as much as you can
into the three gallon container so that there are 2 gallons in the 5 gallon
container. Empty the three gallon and pour the rest of the 5 gallon into the
three and then fill the five. Then pour as much as possible into the three
and you have four gallons left in the 5 gallon container.
***********************************************************************
Name: Mike
Grade: 4
Teacher's Name: Paul Nass
School: Georgetown Day School
Loacation: Washington D.C
First you fill up the 3 gallon jug and pour it into the 5 gallon jug. Then
you fill up the 3 gallon jug again and pour what you can into the 5 gallon
jug. You will notice two things that the 3 gallon jug has 1 gallon in it,
and that the 5 gallon jug is full. Well then you empty the five gallon jug
and pour the 1 gallon of water in it from the 3 gallon jug. Then fill up the
three gallon jug and pour it into the five gallon jug which has been sitting
with 1 gallon in it. Once you pour 3 gallons in it it makes four.
*************************************************************************
David M. Driscoll Joan's 4th Grade Georgetowm Day School Washington D.C.
1.Fill up the 3
2.Dump 3 into 5
3.Fill up the 3
4.Dump 3 into five have 1left over
5.Dump out 5
6.Dump 1 into 5
7. Fill up 3
8.Dump 3 into 5
AND YOU HAVE 4
***********************************************************************
Annie Bolotin Joan's 4th grade Georgetown Day School Washington D.C.
The way I got my answer is by using diagrams.
First you fill up the three gallon container and dump it in to the five
gallon container. Then you fill up the three gallon container again and use
it to fill up the five gallon container. You have one gallon left in the
three gallon container. Dump the five gallon container. Put what is in the
three container in the five. Fill up the three gallon container and dump it
in to the five gallon. You have four gallons.
*********************************************************************
Name: Kate Forscey
Grade: Fourth
Teacher: Paul
School: Georgetown Day School
Location: 4530 MacArthur Blvd., N.W.
Washingon, D.C. 20007
Fill the 5 gallon jug. Pour 3 gallons into the 3 gallon jug. You are left
with 2 gallons in the 5 gallon jug. Empty the 3 gallon jug and pour the 2
gallons from the 5 gallon jug into the 3 gallon jug. Refill the 5 gallon jug
and pour enough water from the 5 gallon jug into the 3 gallon jug. This
would be 1 gallon. Empty the 3 gallon jug and you are left with 4 gallons in
the 5 gallon jug!
************************************************************************
Becky Cisin
teacher Paul Nass
Georgetown Day School
Washington, D.C.
Fill the 3 gallon jug with water.
Pour that into the 5 gallon jug.
Now you have nothing in the 3 gallon jug and 3 gallons in the 5 gallon
jug.
Fill the 3 gallon jug with water.
Pour that into the 5 gallon jug until the 5 gallon jug is full.
Now you have 5 gallons in the 5 gallon jug and 1 gallon in the 3 gallon
jug.
Empty the 5 gallon jug.
Put the 1 gallon from the 3 gallon jug into the 5 gallon jug.
Now the 3 gallon jug is empty and the 5 gallon jug has one gallon in
it.
Fill the 3 gallon jug and pour it into the 5 gallon jug and there you
have 4 gallon.
***********************************************************************
Anna Margush
Grade 4
Home School
Akron, Ohio
margush@uakron.edu
Problem
Fill the 5 gallon jug and pour it carefully into the 3 gallon jug. This
will leave 2 gallons
in the 5 gallon jug. Empty the 3 gallon jug and then pour the 2 gallons
into it. This leaves
room for 1 more gallon. Fill the 5 gallon jug again and pour exactly 1
gallon into the 3
gallon container (just filling it). This leaves the 5 gallon container with
exactly 4
gallons.
Bonus Puzzler
By writing the factors of all of the numbers from 2 to 30, I found exactly
two perfect
numbers:
6 = 1 + 2 + 3
28 = 1 + 2 + 4 + 7 + 14
**********************************************************************
Hello my name is Simone Levien reporting for the problem of the week. I am
in 4th grade in Paul's math class. I go to Georgetown Day School in
Washington D.C.
I got my answer by drawing diagrams and pretending I was holding pitchers.
My answer is: First fill up the 3 gallon container. Then dump it into the
five gallon container. Then fill up the 3 gallon container again and dump it
into the 5 gallon container. You have 1 gallon left in the 3 gallon
container. Then dump out the 5 gallon container back into the pool. Then
dump the 1 gallon leftover from the 3 gallon container into the 5 gallon
container. Then fill up the 3 gallon container again and dump it into the 5
gallon container and you should have 4 gallons of water in the 5 gallon
container!
************************************************************************
Sam Langer
Georgetown Day School
Washington, DC
Teacher: Paul Nass
Grade: 5th
Fill the 5 gallon jug.
Pour water from 5 gallon jug into 3 gallon jug until 3 gallon jug is full.
That leaves 2 gallons in the 5 gallon jug.
Empty the 3 gallon jug.
Pour the 2 gallons from the 5 gallon jug into the 3 gallon jug.
Fill the 5 gallon jug to the 5 gallon line.
Pour water from the 5 gallon jug into the 3 gallon jug until the 3 gallon jug
is full.
Since the 3 gallon jug already has 2 gallons of water in it, that means we
only poured one gallon out of the 5 gallon jug. That leaves 4 gallons of
water in the 5 gallon jug.
****************************************************************************
*****
Brad Jadlowiec
Bonus: 1+2+3=6
1+2+4+7+14=28
****************************************************************************
*****
BRIAN T KING
5TH GRADE
You fill the three gallon jug then dump it into the five gallon jug.
Then fill the three gallon jug again and fill the five gallon jug to the top,
so you have one gallon left in the three gallon jug.
Then dump out all the water in the five gallon jug
and put the one gallon in the five gallon jug.
Then fill the three gallon jug again and dump it into the five gallon jug.
Now you have four gallons in the five gallon jug.
****************************************************************************
Ryan Grace, Kim Fugok, Christine McGowan, and Amanda Tumminelli - Grade 6
Mrs. Brennan - Drexel Hill School of the Holy Child, Drexel Hill, PA
Bonus Question - The two perfect numbers we found were 6 and 28. 6 = 1+2+3
= 6 and 28 = 1+2+14+4+7 = 28
****************************************************************************
Tommy Grace, 5th,Paul Nass, Georgetown Day School, Washington D.C.
Fill the 5 gallon jug. Pour the water from the 5 gallon in to the 3 gallon
jug so that the 5 gallon has 2 gallons in it and the 3 gallon is full. Empty
out the 3 gallon. Pour the 2 gallons from the 5 into the 3 gallon. Fill the
5 gallon. Pour all the water you can from the 5 gallon into the 3 gallon
without spilling any. You now have 4 gallons in the 5 gallon jug.
******************************************************************************
Phillip
Grade 4
Mandarin Oaks Elementary
Jacksonville, FL
You leave the five gallon one empty and then you put water up to the 3
gallon one. Dump it in until it reaches the the 5-gallon point. Then you
have one left. You dump out the five gallons. Put in the one gallon. Then
you fill up the three again and put it into the five gallon and then you
have 4 gallons.
****************************************************************************
*****
Todd Feiler, Matt Spindler, Evan Mossman
4th grade
Fred Rimmel
Kerr Elementary
Pittsburgh, PA
Fill up the 3g container
Pour that into the 5g container
Fill up the 3g container
Pour the 3g into the 5g
Empty the 5g container
Pour 1g from 3g container into the 5g container
Fill up the 3g container and pour into the 5g container
Presto! You now have exactly 4 g.
****************************************************************************
*****
Meghan Ramsey Grade 4 Miss Seager Bagnall School
1-Fill the 3 gallon jug from the pool.
2-Dump the 3 gallon jug into the 5 gallon jug.
3-Fill the 3 gallon jug again.
4-Pour the 3 gallon jug into the 5 gallon jug leaving 1
gallon left in the 3 gallon jug.
5-Dump the 5 gallon jug out.
6-Pour the 1 gallon from the 3 gallon jug into the 5
gallon jug.
7-Fill the 3 gallon jug from the pool.
8-Dump the 3 gallon jug into the 5 gallon jug.
Now you have 4 gallons.
BONUS-6 and 28
EXPLANATION-First , I drew 2 jugs on a
scrap piece of paper. One of the jugs held 5 gallons,
the other held 3 gallons. Then I juggled around the water
until I had 4 gallons. (We both used this strategy)
********************************************************************************
Meghan Lovett Gr. 4 Ms. Seager Bagnall School
1. Fill up the 5 gallon jug with water and pour it into the
empty 3 gallon jug. There will be 2 gallons of water
left in the 5 gallon jug ( 5 gal. - 3 gal. = 2 gal. )
2. Dump out all the water in the 3 gallon jug. Pour the
remaining 2 gallons of water from the 5 gallon jug into the
the empty 3 gallon jug.
3. Fill up the empty 5 gallon jug with water. Pour the water from
the 5 gallon jug into the 3 gallon jug. You will need exactly 1
gallon because there is already 2 gallons of water in the jug.
This will leave exactly 4 gallons of water left in the 5 gallon jug.
Bonus
28, 6.
*******************************************************************************
Grade: 4th
Problem of the Week
School: Georgetown Day School
Student's Name: Luis Mendoza
Teacher: Paul Nass
Solution: Take the three gallon jug fill it with water and put it in the
five gallon jug. Then fill the three gallon jug again with new water. Pour
as much as you can into the five gallon jug, which will leave you with one
gallon in the three gallon jug. Empty out the five gallon jug. Then put the
water from the three gallon jug into the five gallon jug which will leave you
with one gallon in the five gallon jug. Then fill the three gallon jug with
water to the top and pour that water into the five gallon jug. Now you have
four gallons in the five gallon jug.
********************************************************************************
Brittany Kress
Grade 5
Miss Planz
Marzoff Elementary School
Pittsburgh, PA
Fill the 5 gallon jug with water. Then pour it into the 3 gallon
jug. This leaves you with 2 gallons of water in the 5 gallon. Empty
the water in the 3 gallon jug out. Then pour the 2 gallons of water
into the 3 gallon jug. Now fill the 5 gallon jug with water again.
Pour out 1 gallon (enough to fill the 3 gallon jug.) This leaves you
with 4 gallons in the 5 gallon jug.
Bonus: 6,28
6
1,2,3
1+2+3=6
28
1,2,14,7,4
1+2+14+7+4=28
****************************************************************************
******
Nancy Kaye
1. Begin with two empty jugs. 2. Fill the five gallon jug. 3. Fill up the
3
gallon jug from the 5 gallon jug leaving you with 2 gallons in the 5 gallon
jug. 4. Empty the 3 gallon jug. 5. Pour the 2 gallons from the 5 gallon
jug
into the 3 gallon jug. 6. Fill the 5 gallon jug. 7. Pour 1 gallon into
the
3 gallon jug to fill it up from the 5 gallon jug. 8. You now have 4 gallons
in the 5 gallon jug.
Mrs. Bach's 5th grade class in Joyce Kilmer School in Mahwah N.J. It was
the one
with the perfect numbers. Our name are Brett Freeman, Dave Rounds, and Amy
Killough. Our answers were 6 and 28. the factors for 6 were 1,2,3 and the
factors for 28 were 1,2,4,7,14. Although we were the first to get the answer,
everyone else got it too.
1.You fill the jar that holds 3 gallons to the top.
2.You pour the water into the five gallon jar.
3.You fill up the 3 and put as much as the 5 gallon jar can hold(1 gallon
left in the 3).
4.Empty the 5.
5. Pour the one gallon left over in the 3 into the 5.
6. Fill the 3 up and pour it in the 5.
7. And now you have 4 gallons!
Bonus
6: 3+2+1=6
28: 2+4+7+14+1=28
****************************************************************************
Aneil Baron
Paul Nass
Georgetown Day School Washington,DC
3rd grade
Fill up the 5 gallon jug to the line. Dump into the 3 gallon jug to the line
so you have 2 gallons left in the 5 gallon jug. Dump the 3 gallons out .
Pour the 2 gallons into the 3 gallon jug. Fill the 5 gallon jug up again to
the line. Pour 1 gallon of it into the 3 gallon jug which would fill that
one up to the line and leave exactly 4 gallons in the 5 gallon jug.
****************************************************************************
********
Mitchell Malasky grade 4 Joan Foster is my math teacher and
my school is
Georgetown Day School in Washington D.C.
Fill the five gallon jug. Pour three gallons into the
three gallon jug than
empty it. Pour the two remaning gallons in to the three
gallon jug. Fill the
five gallon jug. Then pour as mutch as you can in to the
three gallon jug.
Empty the three gallon jug and you have four gallons.
*****************************************************************************
Laura Fraser - Ms. McCarthy's 5th grade class at Center School
Bonus Puzzler:
1 + 2 + 3 = 6
4+ 7 + 1 + 14 + 2 = 28
*****************************************************************************
Kristin Squires - Mrs. Pensa's third grade center school - Stow Ma
#1 My answer for number one was that you would fill the three gallon
jug, pour it in to the 5 gallon jug. then fill the 3 gallon jug again
and pour it in to the five gallon jug but you would have to leave a
gallon in the 3 gallon jug Then you would empty the 5 gallon jug and
pour the gallon that you had left in the three gallon jug in to the five
gallon jug and fill the three gallon jug again pour that in to the five
gallon jug and you would have 4 gallons in the 5 gallon jar.
#2 I figured that 6 has to be a perfect number because 3+2+1=6 and
that 28 is one because 1+2+4+7+14 =28
**********************************************************************
Sam Hahn - Ms. McCarthy's 4th grade class - Center School Stow MA
Problem #1
The way I solved the problem is:
1. fill the 3 gallon jug
2. empty the 3 gallon jug into the 5 gallon jug
3. fill the 3 gallon jug again and empty what will fit in the 5 gallon jug
4. the 5 gallon jug is now full and the 3 gallon jug has 1 gallon left in it
5. empty the 5 gallon jug
6. pour the 1 gallon remaining in the 3 gallon jug into the 5 gallon jug
7. refill the 3 gallon jug and empty it into the 5 gallon jug.
8. you now have 4 gallons.
Bonus Problem
The way I solved the problem is I checked the factors for each number
from one to thirty. Those whose sum equaled the number are the answers. I
found 6 and 28. The factors for 6 are 1 2 3 6, but we leave out 6. The
factors for 28 are 1 2 4 7 14 28 , but we leave out 28.
****************************************************************************
*********
Ted Powers - Mrs. Pensa's 3rd grade at Center School Stow MA
First I filled up the 5 gallon jug. Then I poured the water from the 5
gallon jug into the 3 gallon jug, leaving 2 gallons in the 5 gallon jug.
I poured the 3 gallons in the 3 gallon jug out and poured the 2 gallons
from the 5 gallon jug into the 3 gallon jug. After that I filled the 5
gallon jug. Then I poured the 5 gallon jug into the 3 gallon jug so that
the 3 gallon jug was filled (it only took 1 gallon). This left the 5
gallon jug with only 4 gallons in it.
****************************************************************************
*********
Sam DeLuca - Mr. Ellsworth's 4th grade - Center School - Stow MA
That problem was very hard this is how I did it:
step 1. Fill the five gallon container.
2. Pour as much of the five gallon container into three gallon
container as you can.
3. Dump the three gallon container.
4. Pour the rest of the five gallon container into the three
gallon container
(you now have 2 gallons in the three gallon container)
5. Fill the five gallon container
6. Repeat step 2
(you now have 4 gallons in the 5 gallon container)
7. Dump the three gallon container.
the way I figured the problem out was with pennies.
******************************************************
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