Elementary POW, October 16-23, 1995
Elementary POW Problems || October-December, 1995 Problems || Elementary POW Main Page
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Elementary Problem of the Week, October 23-27,1995
This week's problem was submitted by Annie Rockenbach, Mount St. Joseph
Academy, Flourtown, Pennsylvania.
I am a 4 digit number.
My tens digit is even.
My hundreds digit is prime.
My ones digit is prime.
Square my ones digit and get my thousands digit.
None of my digits are the same.
The sum of my ones digit and my tens digit equals my hundreds digit.
The product of my ones digit and my tens digit is divisible by 1,2,3,4,6,
and 12.
What number am I?
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This week's Bonus Puzzler was submitted by Mary Golhofer, Mount St. Joseph
Academy, Flourtown, Pennsylvania.
A truck driver is annoyed because his truck is just a half-inch too high to
go through the underpass. He was about to turn back when he had a bright
idea. Ten minutes later he was through the underpass and on his way. What
did he do?
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Correct Solutions submitted by:
Erin Maher
The School in Rose Valley
Pat Comerford-Haley's class in Lancaster, NY:
Ken, Dana, Justin, Carlene, Kevin, Jessica, Lora, Kim, Dan,
Jennifer, Mike, Sam, Lynne, Tony, Tracy, Tim, Ben, Liz, Kaitlin,
Jeff, Kyle, Matt, and Greg. Also fifth graders Jayan and Lisa.
4th grade Math Whiz Kids Linda Kubik
Gifted and Talented Resource Teacher
Grady A. Brown Elementary School
Hillsborough, North Carolina, USA
Jon Anapol in Mrs. Trudell's 3rd grade class at Center School, Stow MA.
Andrew Tomlinson / Grade 5, Mrs. Kelley
Center School
Stow, Massachusetts 01775
Solution from:
Elizabeth Veloz
5th grader
Standard Elementary School
Bakersfield, CA
Jefferson Rd. School:
Greg I.,Julian S., and Katie G.
Ben R. from Mrs. Perreault's room .
Mrs Duggans 4th grade class in Munsey Park School in Manhasset:
Danny Maimone, Matthew Horne and Todd Conis.
Sixth grade students at the Springton Lake Middle School in Media,
Pennsylvania:
Vic Ruggiere and Travis Moore.
The following students submitted creative solutions to the Bonus Puzzler
From Center School, Stow MA:
Bobby Blanton from Mrs. Palmbach's 3rd grade class -
Garrett Jones & Danny Glover.
Alvarado Elementry School
4th and 5th grade
Anna Baugh
Amber Brennan
Tyler Lapoint
Justin Beck
Great job this week! It was really interesting for us to read the
explanations. I'd like to highlight Erin Maher's explanation in particular,
which appears below. Also, Pat Comerford-Haley's class in Lancaster, NY has
promised to challenge us with some puzzles that they've made!
We're looking forward to the challenge. --Ruth
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Erin Maher
The School in Rose Valley
Age 10
First I drew 4 squares. They stood for the numbers. Then I
looked at the directions. They said that the tens digit was
even so I drew an arrow coming out of the third square.
Then I listed all of the single digit numbers that were even
(2,4,6,8) under the arrow. Then I looked at the directions
again. They said that the ones digit was prime so I drew an
arrow coming out of the last square. Then I listed all of the
single digit prime numbers(2,3,5,7) under the arrow. Then I
did the same thing with the hundreds. Then it got
complicated. First I looked at the directions again. They
said to square the ones digit and get the thousands digit.
That meant that 5 and 7 could not be the ones digit because
5 squared is 25 and 7 squared is 49 (both of the numbers are
more than 9). That left 2 and 3. I didn't know which one it
was so I moved on to the tens. I looked at the directions
again. THey said that the product of the ones digit and the
tens digit is divisible by 1,2,3,4,6 and 12 so I knew that
the product of the ones digit and the tens digit was 12. That
meant that the tens digit couldn't be 8 because nothing times
8 = 12. That left 2,4 and 6 for the tens and 2 and 3 for the
ones. The tens digit couldn't be 2 because 6 wasn't a
possibility for the ones digit and 2x6 = 12. That left 4 and
6 for the tens and 2 and 3 for the ones. I knew that 4x3 = 12
and 6x2 = 12 so I drew a line from 4 to 3 and from 6 to 2.
The directions said that if you add the ones digit and the
tens digit you get the hundreds digit. I know that 6+2=8 (not
a prime number) but 4+3=7(a prime number) so I knew that the
ones digit was 3 and that the tens digit was 4. That meant
that the hundreds digit was 7(4+3) and the thousands digit
was 9(3x3) The number was 9743 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Math Wizards who correctly solved the Problem of the Week and the Bonus
Puzzler are:
The following responses are from Pat Comerford-Haley's class in Lancaster,
NY:
Five of our groups arrived at the same answer: 9,743. Each group seemed to
arrive at their answer in a different way...
We did it by trial and error. We guessed a number then went through the
problem clues again and finally came up with the number 9,743. Ken, Dana,
Justin,Carlene
We feel that 9,743 is the correct answer because it fits all of the clues
you gave us. First we found out our ones and tens digits. We did that by
trying all the possible combinations using prime numbers and even numbers
too. Then we added the clues and got hundreds and the thousands digits.
Kevin, Jessica, Lora, Kim
First, we used cards. We put all our cards into one pile and then separated
the prime numbers. We picked out one # from the prime numbers which was 3.
Then we picked out a number from the even pile which was 4. 3+4=7 so the
number 7 is the hundreds digit. In your letter you said that the ones digit
squared equals the thousands digit which would be 9 because 3x3=9. So, our
number is 9,743. Dan, Jennifer, Mike, Sam
We noticed that the ones digit could be 2 or 3. We found that the ones
digit was 3. We found that it was 3 because first we thought it was 2. We
had it until the last clue. So then the number had to be 3. We squared 3 so
our thousands digit came up to be 9. We tried 2 for our tens digit and got
5 for our hundreds digit but it didn't work out in the end because we
couldn't divide the product by 1,2,3,4,6, and 12. So we changed the 2 to 4
for our tens digit and 5 to 7 in the hundreds digit. It all worked out. Our
number is 9,743. Lynne, Tony, Tracy, Tim
9,743 - We found this out by thinking of even numbers starting from 2 and
we worked our way up to 4. By adding 3 for the ones digit to equal 7 for
the hundreds digit
we continued. We got 3 because it was the only number we could add to get a
prime number for the hundred digit. Then we squared 3 and got a 9 for the
thousand digit. But, before we could get the answer, we had to talk and
explain what squared and prime meant. Ben, Liz, Kaitlin, Jeff, Kyle and
Matt
We had two fifth graders who wrote their own number riddle book last year.
We challenged them to solve this problem. Jayan and Lisa both arrived at
the same answer. We were glad they accepted the challenge.
In response to the bonus question:
Greg was the first to suggest that the driver let some air out of the tires
so the truck would be 1/2 inch lower.
Jessica suggested that the driver added extra weight to make the truck
lower to the ground.
Congratulations to the problem creators! You certainly provided us with the
most challenging number riddle we have tackled so far. A few kids were
interested in writing their own riddles so, don't be surprised if we return
the challenge...
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Solution from:
Elizabeth Veloz
5th grader
Standard Elementary School
Bakersfield, CA
My answer to the problem of the week for Oct. 23-27 is 9,743. My teacher
helped me answer the problem. We made a table that showed the one, tens,
hundreds and thousands places and then listed the numbers that might work
in each place. Then we just crossed out the numbers that we knew wouldn't
work. My answer to the bonus puzzler is that the truck driver just let some
of the air out of his tires.
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From: "Jefferson Rd. School"
Answers for this weeks problems submitted by Greg I.,Julian S., and Katie G.
1. the number is 9743
2. Lose a little bit of air out of the tires.
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Danny Maimone, Matthew Horne and Todd Conis. We are in Mrs Duggans 4th
grade class in Munsey Park School in Manhasset. Our answer was hard to get
but we came up with 9743. We had to ask a few questions like what is
prime.We had to change the answer a few times but we think we got it!
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Sixth grade students at the Springton Lake, Middle School in Media,
Pennsylvania. My students worked on the problems individually for homework.
They used their textbooks to clarify vocabulary with which they were
unfamiliar. Not everyone remembered what a prime number was. Although they
had some experience with exponents, they needed help with understanding
what "squared" meant. Pat Hagan
from Vic Ruggiere
The answer is 9743. The way I got the answer is I worked the problem from
end to beginning. The product of the ones and tens which is 3 x 4 (and it
is divisible by 1,2,3,4,6,12) because 7 is prime and 3 squared is 9, which
gave me 9743. I had to find the ones and tens first together with my
hundreds and thousands.
from Travis Moore
I got the answer by working the problem backwards. The product of the ones
and tens is divisible by 1,2,3,4,6,12, which is 3 x 4 because 7 is prime
and 3 squared is 9. Which gave me 9743.
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Alvarado Elementry School
4th and 5th grade
Anna Baugh
Amber Brennan
Tyler Lapoint
Justin Beck
Mystery? Number
The way we did this is we read the directions.And followed them for
each number. Here are the directions: I am a 4 digit number, my tens
digit is even, my hundreds digit is prime, my ones digit is prime, square
my ones digit and get my thousand. None of my digits are the same. The
the sum of my ones digit and tens digit equals my hundreds digit. The
products of my ones digit and my tens digit is divisible by 1,2,3,4,6, and
12. What number am ?. The number we got was 9,743. We had put 4 lines
for the thousands hundreds tens an ones. Under them we put the numbers
that they could be. Example below:
9,743
- - - -
2 0
3 2
5 4
7 6
8
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The following students submitted creative solutions to the Bonus Puzzler:
Bobby Blanton from Center School, Stow MA
Mrs. Palmbach's 3rd grade class -
2. Take the truck route.
Garrett Jones & Danny Glover from Center School, Stow MA
Mrs. Palmbach's 3rd grade class -
2.He took an inch out of each tire.
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