Elementary POW, November 13-17, 1995
Elementary POW Problems || October-December, 1995 Problems || Elementary POW Main Page
******************************************************
Elementary Problem of the Week, November 13-17, 1995
This week's problem was adapted from the November 1995 issue of Mathematics
Teacher.
Although the Pacific Ocean, the Baltic Sea, and the Arctic Ocean are only
three bodies of water, they add up to the seven C's. Substitute a
different digit for each letter. The digit 1 is not used.
PACIFIC
BALTIC
+ ARCTIC
---------
CCCCCCC
(Hint #1: L=0 and A=6, Hint #2: Don't forget what happens if your sum in
a column is greater than 9).
*****************************************************
This week's Bonus Puzzler was submitted by Katie Walder, Mount St. Joseph
Academy, Flourtown, Pennsylvania.
You are cutting a ten-foot pole into equal pieces. If it takes one minute
to make each cut, how long will it take to cut the pole into ten equal
pieces?
******************************************************
Lincoln Elementary School Burlingame, CA Nancy Kaye's 3rd Grade Shane Arslan (POW & Bonus), Christopher P. (POW & Bonus) Springton Lake Middle School Media, PA Pat Hagan's 6th Grade Amanda McGrory (POW), Mike Scheuftan (POW), Travis Moore (POW) Center School Stow, Mass Mrs. McCarthy's 4th Grade Sam Hahn (POW & Bonus), Elise Tarbi (POW & Bonus) Center School Stow, Mass Mrs. Pensa's 3rd Grade Kristin Squires (POW & Bonus) Lisa Simmons (working from home) IHM School Philadelphia, PA The Rice School/La Escuela Rice Houston, Texas Mike Miller's Class Eric Rachlin (POW & Bonus) St. Mary's School Tinconderoga, NY Mr. Hoop's 4th Grade Susan Engin (POW & Bonus), Kaitlyn Pote, Susan Navojosky, Meghan Jebb & Suzanne LeBarron (POW & Bonus), John Olsen, grade 5 (POW & Bonus), Drexel Hill School of the Holy child Drexel Hill, PA Caroline Brennan's 6th Grade Amanda Tumminelli & Ryan Grace (POW & Bonus) Whitehouse Elementary School Jacksonville, Florida Angie Goldsmith's 5th Grade Megan Klaas & Jessica Pounds (POW & Bonus) The School in Rose Valley Rose Valley, PA Michael L. Nowell's 3rd Grade Christopher P. (POW & Bonus), Albert Gentile & Tammy Merjanian (Bonus), Leigh Stefanik & Brian King (Bonus) Underhill School Maidstone, Kent, England Grant Whitaker's Class Carly Crockford (POW), Ashley Philips (POW) Court St. School Lancaster, NY Pat Comerford-Haley's 4th Grade Kurt, Greg, Bethany & Rachel (POW & Bonus), Lora, Kim, Kevin & Jessica (POW & Bonus), Dan, Sam, Mike & Jenny (POW & Bonus), Lynne, Tim, Tracy & Tony (POW & Bonus), Ken, Carlene, Justin & Dana (POW & Bonus), Kaitlin, elizabeth, Ben, Jeff & Kyle (POW & Bonus) Georgetown Day School Washington D.C. Paul Nass's 5th Grade Benjie Achtenberg (POW) Georgetown Day School Washington D.C. Joan Foster's 4th Grade Zachary Sandler (Alternate solution to POW if the digit 1 could be used) Jefferson Road School Pittsford, NY Pat Gaborski's Class Krissie & Jessie (POW & Bonus) Heights Elementary School Sharon, MA Mr. Philip's 6th Grade Math Masters: Jackie Bene', Rachael Ennis, Robert Porter, Tom Wong, & David Goldstein (POW & Bonus) Math Sharks: Erica, Liz, Nicole, Mark & Adam (Bonus) ************************************ The following students attempted the POW but made minor mistakes. Heights Elementary School Sharon, MA Mr. Philip's 6th Grade Math Sharks: Erica, Liz, Nicole, Mark & Adam (Bonus) Munsey Park School Manhasset, NY Marilyn Tahl's Class St. Mary's School Tinconderoga, NY Mr. Hoop's 4th Grade Katie Donovan, Lindsay Hurlburt, Jamie Burris Georgetown Day School Washington, DC Joan Foster's 4th Grade David Driscol, Cyrus Karas, Annie Bolotin & Nathan LaPort The School in Rose Valley Rose Valley, PA Michael L. Nowell's Class Leigh Stefanik & Brian King
********************************************
Dear Ruth:
Here is an answer from Kristin Squires who is in Mrs. Pensa's 3rd grade
class at Center School, Stow, MA.
She spent many hours on solving this problem and didn't give up.
Jody Newman
Library Aide
Center School
1.5,555,555 - I started with the ones position which was all C's.
The only number that added to itself three times would be the number 5.
Then one by one, I figured out the other numbers by adding them up and
carrying the numbers to the next column. So P = 4; L = 0 (given); A = 6
(given); C = 5; i=8 f=9 b=2 r=3 and t=7
4658985 PACIFIC
260785 BALTIC
635785 ARCTIC
2.9 minutes because you only have to cut nine times- after the
ninth cut, you have your tenth piece.
*************************************************
Elise Tarbi from Ms. McCarthy's 4th Grade class at Center School, Stow, MA
1.I solved this problem by looking at the ones position. I tried
#2 and it didn't work. I tried #3 and it didn't work, I tried #4 and it
didn't work but # 5 worked....5 + 5+ 5 = 15 so the letter C=5. Then I
looked at the tens position. What number added three times plus 1 would
equal a five. I found that this would be the number 8 so I = 8. Next I
needed to find out what 2 different numbers plus 2 would equal a number
with a five in it. I had used 5, 8, and 0 and 6 and 1 were given so I had
to choose between 2,3, 4, 7, and 9. I figured out that the letter F = 9 and
the letter T = 7. In the thousands place I knew that one number was 8 and
one number was five and one was 0 plus the 2 I carried over made the answer
5 again with a carry of 1. I knew the ten thousand position had a 5 and a 6
plus the one I carried made 12...so the only thing that could equal fifteen
was a 3 so R=3. In the hundred thousand place we knew the the two 6's and
the 1 that was carried over so 6+6+1=13 and the letter B would have to be
2. Finally, carrying a 1 to the million position and having the final
number having to be a five...I knew that the letter P=4.
PACIFIC = 4,658,985
BALTIC = 260,785
ARCTIC = 635,785
All of this adds up to 5,555,555
2.1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 log
1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9cuts
It took 9 cuts to make 10 pieces so it would be 9 minutes.
*********************************************
Shane Arslan 3rd grade
Lincoln Elementary
School, Burlingame, CA
I put L-0 F-9 I-8 T-7 A-6 C-5 P-4 R-3 and B-2
I put C for 5 because all the rest of the numbers have a 5 at the end. 5, 5
and 5 equals 15. So you carry over a 1 to the 3 I's which would be in the
tens place. 8, 8,8 and 1 equals 25. At the end there is a 5 . So you carry
over a 2. 9, 7,7 and 2 equals 25 and there is a 5 at the end. So you carry
over a 2. 8, 0, 5, 2 equlals 15 and theres a 5 at the end. And you carry
over a 1. 5, 6, 3, 1 equals 15. And that has a 5 at the end. So you carry
over a 1. 6, 2, 6 and 1 equals 15. So you carry over a 1. 4 and 1 equals 5.
That means that there are 7 C's. Because C equals 5 and there where 7
fives.
BONUS It will take 9 minutes and 9 cuts to cut the pole into 10 pieces
because the end piece would be another piece. And that equals 10.
************************************************
Lincoln Elementary School
Burlingame, CA
Christopher P. 3rd grade
Since there is no 1, the First thing I thought c=5 because 5+5+5=15. The
second thing Ithought of was I=8 because 8+8+8=24+1 from the 15=25. then I
thought that T=7 and F=9 7+7+9=23+ the 2 from 25=25. Then since L=0
8+0+5=13+ the 2 from 25=15. Arter that Ithought R could =3, so 5+6+3=14+
the 1 from 15=15. So far I covered 0,3,5,6,7,8,9. Then I thought B=2 so
6+2+6=14+ the 1 from 15=15. Then I thought P=4 so 4+ the 1 from 15=5.
So465895+260785+635785=5555555 and since C=5 there's your answer.
Bonus puzzler's answer:
9 min. because the last cut is providing 2 pieces.
***********************************************
Sam Hahn
Ms. McCarthy's 4th grade class
Center School
Stow MA.
The way I solved the problem was I made a list of the letters that were
used . In the problem it gave two hints. One of them was remember what
happens when a number becomes ten and the second hint was L=0 and A=6.
My strategy was to work from right to left so if a trade is needed it can
be done. I started with the letter C because it was the letter that was
the most used. When it was done it looked like this.
a= 6 b= 2 c= 5 i= 8 f=9 l= 0 t= 7 r= 3 p=4
4658985
260785
+ 635785
________
5555555
bonus puzzle
9 min. because the ninth cut divides the final piece into two parts. So
you don't need to make 10 cuts to get 10 pieces.
****************************************************
Solved by Amanda Tumminelli and Ryan Grace, Grade 6 Teacher: Caroline Brennan
School: Drexel Hill School of the Holy Child, Drexel Hill, PA
Solution: We used a guess and check method plus the two hints. We listed
the digits from 0 - 9 and cross each digit off as we used it. We found that
C = 5, I = 8, T = 7, F = 9, L = 0, A = 6, R = 3, B = 2, P = 4. We enjoyed
doing this problem.
Bonus Solution: Our answer to the bonus problem is that it would take 9
minutes to slice the pole into 10 equal parts. You do not have to cut at
the beginning and at the end. This is how we drew the pole with the nine
cuts.
__l__l__l__l__l__l__l__l__l__
*********************************************
Pat Hagan from Springton Lake Middle School in Media, PA
I gave the 7 C's problem to my sixth grade math class for extra credit.
They had an evening and one math period to work on it. Three of my students
were able to solve the problem. The only hint I gave was to start work on
finding a digit for C first.
Here are their solutions:
P A C I F I C4 6 5 8 9 8 5
B A L T I C2 6 0 7 8 5
+ A R C T I C+ 6 3 5 7 8 5
_______________________________
C C C C C C C5 5 5 5 5 5 5
Amanda McGrory: I tried all the numbers for C and then I came to five. And
that came out right. So every time I came to a new row I add all numbers
until it cam to 5, 15, 25, 35, 45, etc. That is how I got the Pacific,
Baltic and Arctic numbers.
Mike Scheuftan:I got the answer by guessing many times. The trickiest part
was the second row. I did't expect it to get in the twenties.
Travis Moore: I figured out the answer by plugging in numbers. What I did
was start with the C's because in my answer boxes were C's and I had to
find out which numbers equal something that ends with 5 and it was 5. So I
put down 5's in all the C boxes. Then I had a straight row of I's. I went
through all of my numbers until I got to 8. 8 x 3 = 24 plus my one from the
fifteen. Then I just fooled with numbers from 6 on up. When I got to 7 I
added the highest number I could which would be 9. I got to 23 plus the 2
to regroup and I got 25. So the T's became 7's and the F became 9. Just to
let you know this had to do something with 3 seas, the Pacific, Baltic, and
Arctic. The only hint we knew was that L's =0 and A's = 6. The next letters
were I, L and C. I as you know is 8 and L as you just found out is 0 and C
is 5. I didn't need to change anything around but the only thing that I
needed was to add correctly. 8 + 5 = 13 plus 2 = 15. the next letters were
C = 5, A or 6 and R for something. It was 3 plus 1 would altogether equal
15. Next I had A,B and A. I had forgotten about my regrouping so I thought
it was wrong and checked it all over again. Finally, I remembered the
regrouping and B became 2. I added 6 + 2 + 6 = 14 plus 1 gave me 15. Then
only one letter and one number was left with a one to regroup with. So it
was 4 and that solved the problem. One was not used except for regrouping
in this puzzle.
**************************************************
Lisa Simmons
IHM School
Philadelphia, PA
Hi, Mrs. Carver! How are you? I figured out the problem of the week. The
answer is:
4,658,985
260,785
635,785
-----------------
5,555,555
It took me a couple tries, but I finally found my mistake. Thank you for
reading my answer and helping me arrive at the correct one. ----Lisa
Simmons
*****************************************************
My name is Susan Engin, and here is my answer. I'm, in 4th grade at St.
Mary's School, Ticonderoga, New York in Mr. Hoops class.
.
I had to find what can fit with the problem and the awser.The awser p is 4
A is6 C is 5 I is8 F is 9 B is 2 L is0 T is 7
R is3And the bonus is 9 minute.
4658985
260785
+635785
________
5555555
******************************************************
Whitehouse Elementary School
Jacksonville, Florida
Angie Goldsmith's 5th Grade
Megan Klaas & Jessica Pounds
Since C had to be the same number,we found a digit that when added three
times would equal the same number in the answer.By plugging in diffrent
numbers we found that 5 is the only number that fits the rule. Then we knew
that all our other places had to equal a number with 5 as the last digit.
Then all we did was plug in numbers.
C=5 L=0 A=6 P=4 B=2 T=7 R=3 F=9 I=8
4658985
260785
+ 635785
-----------
5555555
BONUS ANSWER
First, we drew a log,then we divied the log into ten equal pieces.Next, we
counted the cuts we made.Finally,we came up with the answer,which is 9
minutes.
*******************************************************
Albert Gentile, age 11
Tammy Merjanian, age 11
The School in Rose Valley
Bonus Puzzle Answer
The answer is 9 minutes.
We got this answer by drawing a picture and using a ruler.
First we thought it was 10. We saw that you wouldn't cut
off the ends of the pole so you would need 9 cuts.
****************************************************
Court St. School
Lancaster, NY
Pat Comerford-Haley's 4th Grade
Dear Katie, We were all able to answer your puzzler this week. Here are two
of the written responses we wrote: First, we drew the ten foot log and then
we drew nine cuts going down on the log and got nine cuts and we got nine
minutes. Kurt, Greg, Bethany, and Rachel
First, we made a line and pretended it was a ten foot pole. We split it
into ten equal parts. Then, for each line (which stands for a cut) we
counted one minute. When we were done, we got nine minutes. That's how we g
got our answer.
Lora, Kim, Kevin, and Jessica
For the POW we were all able to solve the problem. Lora, Kevin,Jessica, and
Kim were the first to solve the problem but we all continued until we were
successful. Here are some of our written responses:
C is five because it is the only number you can add three times and get a
number with a 5. I is 8 because 8+8+8=24 / 24+1=25 and then the 2 would be
carried to the next column.
F is 9 and T should be 2 so 9+7+7=23 +2= 25 then carry the 2. R should be 3
so 6+3+5=14 +1=15. Carry the 1. B should be 2 so 6+6+2=14 +1=15. Carry the
1. P has to be 4 so 4+1=5.
Dan, Sam, Mike, and Jenny
We tried trial and error a lot until someone finally figured out a number
that seemed to work. C=5
L=0
A=6
I=8
F=9
T=7
R=3
P=4
B=2
Lynne, Tim, Tracy, and Tony
Ken, Carlene, Justin, and Dana
We found out that C=5 . We thought of all the numbers and added them 3
times and 5 was the only one that worked. We did trial and error for I.
Finally, we found I=8 because if you add 8+8+8 you get 24 then add the 1
you carried from the C's. Then we had to find out what T and F was. We
thought that we had to find out two numbers to equal 23 because we carried
2 from the I's. We know that the only three numbers to equal 23 were 9,7,.
That equals 23 but we had to add the 2 that we carried which would equal 25
then we carried 2 over to above the I. But we know that I=8 and that L=0
and that C=5 so we added them together and got 15 and we carried the 1 to
above the C. We know that C=5 and A=6 because you told us. So we had to
find out whar R=. We added 5+6 and got 11 so in that case we had to get a
number to add on to 11 that would get us to 15. We found the answer was 3
because we had a 1 that we carried. So we carried the 1 to above the P. We
found that P=4 because we had the 1 that we carried and that would get us
to 5. Our answer is 5,555,555.
Your math buddies Kaitlin, Elizabeth, Ben, Jeff, and Kyle.
******************************************************
My name is Benjie Achtenberg. I go to Georgetown Day School in Washington
DC. I am in
5th grade. My math teacher is Paul Nass.The way I figured this problem out
is I detirmaned that
the c's were 5 by adding the c's on the far left of the problem. It can't
be 4+4+4 because that is 12
and that is too low. I figured the rest of the numbers off the 5's.
PACIFIC
BALTIC
+ARCTIC
CCCCCCC
A=6
B=2
C=5
L=0
I=8
P=4
T=7
R=3
F=9
4658985
260785
+635785
5555555
************************************************
ZACHARY SANDLER ,4th grade , Joan Foster , Georgetown Day School,
Washington, DC
If L was not given as zero and the digit one could be used, this is an
alternate solution.
PACIFIC4658985P=4 L=1 A=6 T=2C=5R=3
BALTIC261285I=8 F=9B= 2
+ARCTIC+635285
--------------------
CCCCCCC5555555
*************************************************
Math MastersNovember 15, 1995
Mr.Philips Gr. 6Heights Elem.
Sharon, MA
4658985We got our answer through process of elimination.
260785We picked 5 for c because 5 times 3 =15 and 15 is the
+ 635785only number that fits. From there on we just tried to see
5,555,555what fit and if it did we used it.
A=6, B=2, C=5, F=9, I=8, L=0, P=4, R=3, T=7
Bonus question
It takes 9 cuts to get 10 pieces, so therefore it takes 9 m
********************************************
[Privacy Policy] [Terms of Use]
Home || The Math Library || Quick Reference || Search || Help
The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies.