Elementary POW, November 27 - December 1, 1995
Elementary POW Problems || October-December, 1995 Problems || Elementary POW Main Page
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We have two number puzzles and one bonus puzzle this week, all created by
elementary students.
This week's first problem was created by Jayan, a 5th grader in Mrs. Pat
Comerford-Haley's class, Court St. School, Lancaster, NY.
I am a seven digit number.
I am an even number.
My tens digit is prime.
Add my ones digit and my tens digit and you get my millions digit.
Divide my ones digit by my tens digit and get my hundreds digit.
Add my hundred thousands digit and my ten thousands digit and get my
thousands digit.
Add my tens digit and my hundreds digit to get my thousands digit.
Subtract my hundreds digit from my ones digit and get my hundred thousands
digit.
Multiply my tens digit by itself and get my millions digit.
My ones digit is even.
My hundred thousands digit is also even. None of my digits are the same.
Hope you enjoy this one!
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The second number puzzle was submitted by Ashley Phillips of Underhill
School, Maidstone, Kent, England, Mr. Grant Whitaker's class.
UNE
+ DEUX
-------
TROIS
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This week's Bonus Puzzler was submitted by Lora, a 5th grader in Mrs. Pat
Comerford-Haley's class, Court St. School, Lancaster, NY.
There was once a cowboy. He rode into town on Friday. He stayed 3 days and
left on Friday. How is this possible?
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Problem Solvers, Jessica Pounds & Megan Klaas Whitehouse Elementary Jacksonville,Florida Mr.Roberts' fifth grade class (Bonus) *********************************************** Ashley Phillips Underhill School Maidstone,Kent,England (POW #1 and Bonus) ************************************************ Becky Cisin Paul Nass Fourth Grade Georgetown Day School Washington, DC (POW #2, Bonus) *********************************************** Sade' Hooks 5th grade Laura Chlopecki (Homeroom) Paul Nass ( Math Teacher) Georgetown Day School Washington D.C. (Bonus) *********************************************** Zachary Sandler Georgetown Day School Washington, DC, Paul Nass Joan Foster (POW #2) **************************************************** Kevin Ohashi Fourth Grade Georgetown Day School Joan Foster (POW #2, Bonus) ******************************************* Cyrus Kharas Georgtown Day School Washington D.C. Paul's 4'th grade math (POW #1, Bonus) ******************************************* Rebecca Eiseman Grade 3, Mrs. Kaye Lincoln Elementary, Burlingame (Bonus) ******************************************* Student names: Ryan Grace, Amanda Tumminelli, Kim Fugok, Christine McGowan, Grade 6, Mrs. Brennan, Drexel Hill School of the Holy Child, Drexel Hill, PA (POW #2, Bonus) ******************************************* Mrs. Palmbach's 3rd grade class - Center School - Stow MA Peter Mangolds (POW #2, Bonus) Robert Golder & Danny Glover (POW #2, Bonus) ********************************************* Mrs. Pensa's 3rd grade class at Center School - STOW MA Kristin Squires (POW #1) ******************************************** Mrs. O'Connell's 5th grade class - Center School - Stow MA Jenny Sadler (POW #1) *********************************************** Mrs. O'Connell's 5th Grade - Center School - Stow MA Jeanette Kurian & Julia Broyer (POW #1) ************************************************ Dani Forman 4th grade Paul's Math class Georgetown Day School Washington D.C. (POW #1, POW #2, Bonus) ************************************************ Benjie Achtenberg 5th grade Paul Nass Georgetown Day School Washington, DC. (POW #2) ************************************************** Crystal Alston 5th grade Burchfield Elementary School Pittsburgh PA (POW #1, POW #2, Bonus) *************************************************** Heights Elementary School Sharon, Massachusetts Mr. Philips Grade 6 Math Dragons: Shyam, Natalie, Lia, Rabia, Steven (POW #1, Bonus) Math Frogs: Evan, Joe, Nikki, Steve, Rachel (POW #1, POW #2, Bonus) Math Machine: Kayla, Jamie, Mike, Evin, Matt (POW #1, Bonus) Math Masters: Jackie, Tom, Robert, David, Rachel (POW #1, POW #2, Bonus) Math Sharks: Adam, Erika, Elizabeth, Mark, Nicole (POW #1, Bonus) ************************************************** Dan, Peter, Krissy, and Jessie eff. Rd. School Pittsford, N.Y. (POW #1, POW #2, Bonus) ***************************************** Danny Maimone,Matthew Horne and Brandon Perkins (POW #1, POW #2) ********************************************* Ms. McCarthy's 4th grade - Center School - Stow MA Eric Winters (Bonus) Craig Vaccaro (POW #1, POW #2, Bonus) Joey Morrissey (Bonus) Sam Hahn (POW #1, POW #2, Bonus) ********************************************* Peter Killian Rice Mr. Miller's Class (POW #1) ********************************************** Nichole Howard, Amy Reynolds, and Sarah Shahadi (POW #1)
Dear Problem Solvers.
Your work just keeps getting better and better. The explanations to
this week's problems were really good. Thanks again to Jayan from Pat
Comerford-Haley's 4th grade class at Court St. School, Lancaster, NY for
his original number puzzle. I know I really enjoyed solving it. Lora's
bonus puzzler was also a lot of fun.
I was amazed at the number of different possible answers for the
French number problem. Dani Forman, a 4th grader in Paul Nass' class at
Georgetown Day School in Washington D. C. found four different solutions.
Thanks again to Ashley Phillips from Underhill School, Maidstone, Kent,
England for sending it to us.
Keep up the great work!
-Ruth Carver and Matt Gehrett
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Elementary POW Highlighted Solutions November 27th - December 1st
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My name is Ashley Phillips and I am from Underhill
School,Maidstone,Kent,England.This is my solution to your problem.
9 , 4 1 5 , 2 3 6
- - - - - - -
7 1 3 1+2 1 2(NOT2) 2
6 3 4 1+3 2 3 4
8 5 5 2+2 3 5 6
9 7 1 2+3 4 7 8
2 2 3+2
4 3+3
6 4+2
4+3
Solution to French Arithmetic:
5 7 6
+ 9 6 5 8
----------
1 0 2 3 4
Thank you for including this puzzle in your POW
Is the horse called Friday? !
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His horse was named Friday.
Becky Cisin
My math teach is Paul Nass
Fourth Grade
Georgetown Day School
Washington, DC
The answer to the first elementary problem of the week is
9,415,236
Becky Cisin
My math teacher is Paul Nass
Grade 4
Georgetown Day School
Washington, DC
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My answer to the Bonus Puzzler the week of November 27 - December 1: his
horse's name is Friday, because three days after Friday is Monday and
usually cowboys ride horses.
Sade' Hooks 5th grade Laura Chlopecki (Homeroom) Paul Nass ( Math Teacher)
Georgetown Day School Washington D.C.
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Hello! I'm Zachary Sandler, from Georgetown Day School, in Washington, DC,
and my math teacher is Paul Nass, and I am in Joan's 4th grade class. Here
is how I figured out the problem:
First, I thought, since the T of TROIS was the only letter in the problem
which was in the 10,000 column, I said T must equal 1. Next, I thought,
since the highest sum of two one-digit numbers which are not the same is 17,
(9+8), I could only carry 1 into the thousands column, so I said D must equal
9. Therefore, R must equal 0. Then I had to figure out from the ones
column, up. I figured out the rest from there.
Here is my answer:
UNE 675
+DEUX +9568
------ -------
TROIS 10243
D=9 E=5 I=4 N=7 0=2 R=0 S=3 T=1 U=6 X=8
Kevin Ohashi
Fourth Grade
Georgetown Day School
Joan foster is my teacher
************************************************
e=5 x=1 n=4 u=7 d=9 s=6 i=1 o=3 r=0
t=1
UNE *(This would be correct only of 2 different letters
+ DEUX could represent the same digit--x=1 and i=1)
-------
TROIS
There was once a cowboy. He rode into town on Friday. He stayed 3 days and
left on Friday. How is this possible?
His horses name was Friday .
Kevin Ohashi,
Fourth Geogetown Day School Joan Foster
*******************************************
9415236
I just tried almost every one digit number and figured it out. My name
is Cyrus Kharas I go to Georgtown Day School in Washington D.C. U.S.A.in
Paul's 4'th grade math and for the third Problem of the week Friday is his
horse and for that I just figured it out
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Hi I am Rebecca,
at first I thought it would be hard,but once I read it, I started
thinking
My dad helped me, he said what else can Friday mean? I shruged.He told me
about
two police men.One was named Friday so I figured it was his horse that he
rode
on.
Rebecca Eiseman
Grade 3, Mrs. Kaye
Lincoln Elementary, Burlingame
Nancy Kaye
Lincoln Elementary School
Burlingame, CA 94010
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Answer to the second number puzzle and bonus.
Student names: Ryan Grace, Amanda Tumminelli, Kim Fugok, Christine
McGowan, Grade 6, Mrs. Brennan, Drexel Hill School of the Holy Child,
Drexel Hill, PA
Amanda, a French student, noticed that une was the French word for one,
deux was the French word for two, and trois was the French word for three.
So, 1 + 2 = 3. Then we looked further at the problem to see if the letters
represented a number. We found the following numbers to represent the
following letters: U = 8, N = 4, E = 7, D = 9, X = 5, T = 1, R = 0, O = 6,
I = 3, S = 2. So, 847 + 9,785 = 10,632.
Bonus: If the cowboy rode into town ON Friday and left ON Friday and spent
3 days, the only possible solution is that Friday is the name of his horse.
Caroline Brennan,
Math and Reading Teacher
Drexel Hill School of the Holy Child
450 Penn Avenue
Drexel Hill, Pa.19026
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Peter Mangolds - Mrs. Palmbach's 3rd grade class - Center School - Stow MA
3. I once heard the joke and the answer was the cowboy's horse was
named Friday.
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Robert Golder & Danny Glover- Mrs. Palmbach's 3rd grade class -Center
School Stow MA
3. 3 days after Friday would be Monday, so the horse's name must be
Friday.
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Kristin Squires - Mrs. Pensa's 3rd grade class at Center School - STOW MA
1. I made a grid of numbers like this
0 0 0 0 0 0 0
1 1 1 1 1 1 1
2 2 2 2 2 2 2
3 3 3 3 3 3 3
4 4 4 4 4 4 4
5 5 5 5 5 5 5
6 6 6 6 6 6 6
7 7 7 7 7 7 7
8 8 8 8 8 8 8
9 9 9 9 9 9 9
I knew it was an even number so the ones had to be 2, 4, 6, 8, 0. I knew
that the tens digit was prime so that crossed out 4,6,8,9, I knew that
it was a seven digit number so two numbers weren't used and I knew that
if you subtract my hundreds digit from my ones digit you will get my
hundred thousand digit so that excluded 9 from the hundreds column.
When I saw that none of the numbers were the same I knew that as soon as
I saw that a certain column had a certain number, I could exclude that
number from every other column. So soon some of the other clues that
were almost not important in the beginning began to finish up the
puzzle, like when I found out that my ones digit was 6 that excluded
9,8,7,6, from my hundreds column. From the clue start my hundreds digit
from my ones digit and get my hundred thousands digit. So I kept
excluding and finally I got my answer 9,415,236.
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Jenny Sadler - Mrs. O'Connell's 5th grade class - Center School - Stow MA
1. First I made a chart of 7 blocks.
I knew the ones digit had to be even. It was either 4, 6, or 8
I listed all the prime numbers with one digit 2,3,5, and 9
Then I made a guess of the ones and tens digit, and added them together
I put that number in the millions box 6 was the ones digit and the tens
digit was 3
Then I skipped to the bottom of the clues and made sure none of the
numbers were the same
I also knew my hundred thousands digit had to be even.
I guessed it was 4
If I could find the ten thousand digit, I could find out the thousands digit
At first I thought 3, but then I thought 1
By now, I had the number - 41 - - 36
The ones digit and the tens digit added up to 9, so I put 9 in the
millions box
4+1= 5 That means that the ten thousands digit is 5
3 +?=5 2 of course
That puts 2 in the thousands place
The number now is 9,415,236
That is the final number.
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Jeanette Kurian & Julia Broyer Mrs. O'Connell's 5th Grade - Center
School - Stow MA
Question 1:
1. First we made seven columns. We wrote what we knew about them by the
clues.
2. We knew that the 1's column was even and the 10's column was prime.
3. Then we took the 9th & 4th clue and figured out that the 1's column
was 6 and the 10's column was 3.
4. Then we added the 1's and 10's column to get the millions column which
is 9.
5. Then we divided the 1's digit by the 10's digit and got 2 for the
hundreds column.
6. Then we added the 10's and 100's to get 5, the 1000's digit.
7. Then we subtracted our 100's digit from our 1's digit to get 4,
our100,000 digit.
8. The hundred thousands digit plus the ten thousands digit had to equal 5.
The ten thousands digit is 1.
9. The number is 9,415,236
************************************************
DANI FORMAN. 4TH GRADE PAUL'S MATH CLASS
GEORGETOWN DAY SCHOOL WASHINGTON D.C.
NUMBER PUZZLE #1
9,415,236 DANI FORMAN
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PUZZLE # 2
I HAVE 3 DIFFERENT ANSWERS
ANSWER #1 U=8 N=7 E=4 D=9 X=2 T=1 R=0 O=3 I=5 S=6
ANSWER #2 U=8 N=4 E=7 D=9 X=5 T=1 R=0 O=6 I=3 S=2
ANSWER#3 U=7 N=5 E=8 D=9 X=4 T=1 R=0 O=6 I=3 S=2
ANSWER #4 U=7 N=4 E=8 D=9 X=5 T=1 R=0 O=6 I=2
S=3
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PUZZLE #3
HIS HORSE WAS NAMED FRIDAY
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My name is Benjie Achtenberg. I am in the 5th grade. My math teacher is
Paul Nass. I go to
Georgetown Day School in Washington, DC.
une 874
The answer to the problem + deux is + 9,482 .
trois 10,356
I tried to isolate d and t.
u + e has to equal a two-digit number because d has to have something added
to it to equal the
two-digit number that is t and r.
The most e + u could ever be is 17 (9+8). The highest number carried over
would be 1. The only
number d could possibly be is 9. Therefore d has to be 9 and t has to be 1.
Once I figured out that d was 9 and t was 1 I went to the hundreds column.
e+u have to equal a
number 10 or above. And we also know that if e + u equals 10 or above then
the 1 we carried
from the hundreds column equals 10 which means that r has to be 0.
u and e added together could not be more than 15 because the two highest
numbers that are left
are 8 and 7 (8+7=15). So we started with 8 at the top and started with 2 at
the bottom. 8+2=10
so that won't work because r is already 0.
Then I was able to figure out the other numbers.
**************************************************
Hello my name is Crystal Alston. I am a 5th grade student in Burchfield
elementary school in Pittsburgh PA. Here are my answers to your problems.
****week of Nov. 27th to Dec. 1st****
1.) 9,415,236
3.) The cowboy rode into town on a horse named Friday. Stayed for
three days and left on the same horse.
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Heights Elementary School
Sharon, Massachusetts
Mr. Philips
Grade 6
Math Dragons: Shyam, Natalie, Lia, Rabia, Steven
Our answer to the 7 digit question is 9415236.
We first picked an even number for the ones place with trial and error
and we got 6. We did the same thing again except this time we picked a
prime number which was 3. Then we added the ones digit and the tens digit
and got the millions digit which was 9. We did trial and error again for
the hundreds place and we picked a number not used which was 2. We added
the tens and hundreds digit and got the thousands digit which was 5. For
the ten thousand place and the hundred thousand place we picked 2 numbers
to add to the thousands digit and we got our answer.
We could not solve the second problem
The answer to the bonus is that the man's horse is named Friday.
**************************************************
Heights Elementary School
Sharon, Massachusetts
Mr. Philips
Grade 6
Math Frogs: Evan, Joe, Nikki, Steve, Rachel.
The answer to the problem is 9,415,236.
To figure out the answer, we looked at the clues, step by step. We knew
it was an even number which means the ones digit had to be 2,4,6, or 8.
And since the tens digit had to be prime, it could only be 1,2,3,5 or 7.
We chose numbers and looked to see if they fit with all the clues and
only changed one number at a time. So we ended up using a 6 for the ones
place and a 3 for the tens and a 9 for the millions place. The next clue
said if you divide the ones by the tens place you get the hundreds which
was 2. Basically after that we did guess and check for the hundred
thousand, which was 4, ten thousand which was 1 and the thousands place
which was 5. The rest of the clues helped us figure out the rest.
The answer to the second problem
UNE 576
+
DEUX is +9658
------- ----------
TROIS 10234
The way we solved the second problem was basically guess and check. But
when we found that it was wrong we only changed one at a time. It took a
lot of work but we finally got the answer.
* Bonus*
The answer to the bonus was that the horse's name was Friday.
********************************************
Heights Elementary School
Sharon, Massachusetts
Mr. Philips
Grade 6
Math Machine: Kayla, Jamie, Mike, Evin, Matt
The answer to the problem is 9,415,236.
We figured this out because the tens digit had to be a prime which could
only be numbers 1, 2, 3, 5, and 7. The ones digit could only be numbers
2, 4, 6, and 8 because it is even. We found a combination 3 for the tens
digit and 6 for the ones digit and 3+6=9. So 9 is in the millions
place.We checked this because 3 times 3 equals nine and knew it was
correct and that it is the millions place. Then we did 3 divided by 6
and 2 was our answer so 2 is our hundreds. The tens plus the hundreds
digit equals the thousands digit. So 3+2=5. Then it was the ones digit -
the hundreds digit equals the hundred thousands digit. So 6+2=4. Finally
it says hundred thousands digit+ the ten thousands digit = the thousands
digit so 5-4=1.
We could not get the answer to the second problem.
The answer to the bonus problem was that the man rode in on his horse
which was named Friday.
************************************************
Heights Elementary School
Sharon, Massachusetts
Mr. Philips
Grade 6
Math Masters: Jackie, Tom, Robert, David, Rachel
The answer to the problem is 9,415,236.
We know that the tens digit has to be 1, 2, 3, 5, or , 7 because
you said that it had to be a prime number. Then you said that the ten's
digit times itself equals the millions digit. 7x7=49, so that can't be it
.5x5=25, so that can't be it either. 3x3=9, so that is a possible number.
2x2=4, so that is another possibility. 1x1=1, but that wouldn't work
because the same number would be in 2 places. We decided to try 9 as the
milloins digit and 3 as the ten's digit. Then you said the one's digit
plus the ten's digit = the millions digit (_+3=9). So the one's digit has
to be 6, since nothing else fits. Then you said to divide the ten's digit
by the one's digit and your answer would be the hundreds digit. 6 divided
by 3 is 2, so the hundred's digit is 2. After that you said the ten's
digit plus the hundreds digit equals the thousands digit. 3+2=5. Ones
digit minus the hundreds digit equals the hundred thousnds digit
6-2=4.Then you said the hundred thousand digit + the ten thousand digit =
the thousands digit. So the ten thousands digit has to be 1,7,or, 8 since
all the other numbers are used. 4+_ =5. The only number that fits is 1.
The answer to the second problem
UNE 758
+DEUX is +9874
________ ______
TROIS 10632
We got our answer through a lot of trial and error.
The answer to the bonus problem is that the man's horse is named Friday.
********************************************
Heights Elementary School
Sharon, Massachusetts
Mr. Philips
Grade 6
Math Sharks: Adam, Erika, Elizabeth, Mark, Nicole
The answer to the problem is 9,415,236.
We arrived at this answer by first finding the digit in the tens place.
The way we found the digit is by finding all the single digit prime
numbers. After that we tried each number with the clues and found that
only the number 3 fit. Then we multiplied the tens digit by itself and
got the number 9 for the millions place. Next we found the ones digit by
finding a number that when added to 3 equals 9. The number we found was
6. Then we divided the ones digit by the tens digit and found the
hundreds digit which is the number 2. Next we added the tens digit to
the hundreds digit and got the number 5 for the thousands digit. Then we
subtracted the ones digit from the thousands digit and got the number 1
for the ten thousands digit . Next we came to the conclusion that when
the number 4 is added to 1, it will equal 5. That is how we arrived at
our answer.
We could not solve the second problem.
The answer to the bonus is that the horse's name is Friday.
****************************************
This is Dan, Peter, Krissy, and Jessie from Jeff. Rd. School, Pittsford,
N.Y. Our answer is 9,415,236. This problem was kind of hard. We learned
prime numbers in 4th grade. Our answer to the second problem is 1+2=3.
The bonus answer is,"the horse's name was Friday!"
*****************************************
ADDITION TO PREVIOUS ANSWER:
Kristin Squires - Ms. Pensa's 3rd grade - Center School - Stow MA
1. answer sent already
2. no answer given
3. the horses name was Friday so it Is possible .
*********************************************
Eric Winters - Ms. McCarthy's 4th grade - Center School - Stow MA
1. no answer given
2. no answer given
3. My answer is that the horses name is Friday.
*********************************************
Craig Vaccaro
1. First I looked over all the clues and narrowed the possibilities
to a couple of numbers that might fit. Next I picked out some of the
numbers and tried them, if they didn't work with the other clues I'd pick
new numbers. Finally the answer I came to was:
9,415,236.
2. For the second number puzzle I kept on saying the words and
then it dawned on me that UNE, DEUX, and TROIS are the numbers one, two,
and three in French. So what I came to in the end was one plus two
equals three.
Bonus Puzzler. At first it didn't make sense to me how a week could pass
in three days but then I found out that if the cowboy's horse's name was
Friday that he could ride in and out on "Friday".
***********************************************
Joey Morrissey
1. no answer given
2. no answer given
3. The horse's name was Friday.
***********************************************
Sam Hahn
1. The way I solved the problem was I looked at all the prime and
even numbers and tried all the combinations and
m, hth, tth, th,h, t, o
t prime
t+o=m
t:- (divided by) o=h
hth=th=tth
t=h=th
h-o=hth
txt=m
o even
hth even
answer is: 9,415,236
2. This was in French...
1
+2
____
3
3. The horse's name was Friday.
*********************************************
I found out the answer for the first math problem and it is
9415236 and I got it by going back and changing what is needed to
be changed. I went though the instructions one last time to
make sure the answerwas right.
I am comfused about the second one because all you
give us letters and no instructions.
But thank you for giving
us puzzlers to be challenged with.
Rice School Mr. Miller's class C204
Do I get any thing for geting the answer right?
Sencerely,
Peter Kilian Rice
**********************************************
Nichole Howard, Amy Reynolds, and Sarah Shahadi: 9,415,236
This is how we solved the problem... We followed the steps that you gave us
but we got stuck on the hundreds, ten, and ones. We also got stuck on the
millions, but we took some guesses and checked them with your steps and we
think this one is right.
**********************************************
DANI FORMAN. 4TH GRADE PAUL'S MATH CLASS
GEORGETOWN DAY SCHOOL WASHINGTON D.C.
NUMBER PUZZLE #1
9,415,236 DANI FORMAN
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PUZZLE # 2
I HAVE 3 DIFFERENT ANSWERS
ANSWER #1 U=8 N=7 E=4 D=9 X=2 T=1 R=0 O=3 I=5 S=6
ANSWER #2 U=8 N=4 E=7 D=9 X=5 T=1 R=0 O=6 I=3 S=2
ANSWER#3 U=7 N=5 E=8 D=9 X=4 T=1 R=0 O=6 I=3 S=2
ANSWER #4 U=7 N=4 E=8 D=9 X=5 T=1 R=0 O=6 I=2
S=3
----------------------------------------------------------------------------
PUZZLE #3
HIS HORSE WAS NAMED FRIDAY
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