Elementary POW, April 7-11, 1997
Elem POW Problems || March - June '97 Problems || Elem POW Main Page
Each of the nine letters in the circles below stands for one of the numbers one through nine, but no two letters stand for the same number. Using the clues, can you deduce the number represented by each letter?
- P is evenly divisible by U, which isn't 1.
- S + 3 = X.
- Q, S, T, and X are prime numbers.
- V is evenly divisible by S.
- Q, P, and W are consecutive numbers in ascending order.
When you explain your answer, pretend that the reader wasn't able to solve the puzzle. Lead us through the steps for figuring out what each number must be.
This week's mentors are from Lisa Lavelle's Precalculus class at the Maret School in Washington, D.C.
We received approximately 100 solutions, including one from Auckland, New Zealand and several from Canada. We were also pleased to receive several answers from home schoolers!Highlighted Solutions:
Daniel Kahn, grade 3
Mrs. Berendsen
e-mail:fhcdsco2@gti.net
Far Hills Country Day School
Far Hills, NJI made a grid and used process of elimination to solve the problem. I will show it right here.
P Q R S T U V W X Key 1 x x o x x x x x x no = x 2 x x x o x x x x x yes = o 3 x x x x o x x x x 4 x x x x x o x x x 5 x x x x x x x x o 6 x x x x x x o x x 7 x o x x x x x x x 8 o x x x x x x x x 9 x x x x x x x o xS+3=R. In other words, R-S=3. There are three numbers in between. R and S are both primes. There must be one even and one odd. 2 is the only even prime. 2+3=5. 2-3 is a negative number. Therefore, S=2 and R=5.
Submitted by The Irish Duo from the W. Edward Balmer School in
Northbridge, MA.
P = 8 Q = 7 R = 1 S = 2 T = 3 U = 4 V = 6 W = 9 X = 5S and x both prime
only 2 prime numbers that have a difference of 3 are 2 and 5
so S = 2 and X = 5Q is prime, only three numbers in ascending order (QPW) that one of them is prime are 7, 8, 9. So Q = 7 P = 8 W = 9
P is evenly divisible by U already used the number 2 so U must = 4
T is prime so T = 3
V = 6 because it must be evenly divisible by S (2)
R = 1 because it is the only number left
Brendan Molaghan, Marlon Adams, and Eric LaValley
Grade six
Mr. Crescitelli
crescitj@nps.northampton.ma.us
J.F.K. Middle School, Bridge Road, Northampton, MA(Regina, Lindsi, & Amy and Alma, Hannah, Rebecca, & Peter from the same school also had a great explanation)
First we read through all of the sentences which gave information, then we made two lists: One of all the numbers, one through nine, and another list of all of the given numbers. Each time we got a number/letter pair we would cross out a number and letter. Sentence number three told us that "Q", S, T, and X were all prime numbers. In sentence five it said that "Q", "P" and "W" were consecutive numbers, ascending. Since "P" and "W" weren't prime we knew we could only go up from 7 because, looking at the number line, you notice that if you start at 2, 3, or 5 then you run into other prime numbers. 7,8,9 is the only possible way it works.
Steps 1, 2, and 4 led us to believe that our theory was definitely true because the numbers left 1,2,3,4,5,6, fit the steps perfectly. Step 1 said "P" is evenly divisible by "U" and if "P" was 8, "U" could be either 2 or 4. We went with 4 because according to step 3, "U" wasn't a prime number. 4 isn't prime and 2 is. Step 2 also proved to be true because "S" which is 2, plus the given "3" equals five. The letter "X" represented that number; therefore "X" equals five. As it tells us, "X" is a prime number and we know 5 to be a prime number.
Step 4 came last. It states that "V" is divisible by "S". This is true in our case because "V" being 6 is easily divisible by "S" which is 2. Thus giving us the answer:
R=1, S=2, T=3, U=4, X=5, V=6, Q=7, P=8, and W=9.
R=1 because the steps say nothing about either one so they obviously go together.
(brief solution)
Mary
Three Oaks Elementary School
Three Oaks MI
Teacher: Carter
Grade 5p=8; q=7; r=1; s=2; t=3; u=4; x=6; w=9; x=5
Prime number 2S, 3T, 5X, 7Q
V divisible by S 6 divided by 2 = 3
PQW consecutive--7,8,9
S=3=X 2+3=5
P divisible by U
8 divided by 4 = 2
Correct Solutions were submitted by:
Leslie Faylor Grade 3, Mr. Geschel Western Salisbury School Allentown, PA ------------------------ Daniel Kahn Grade 3, Mrs. Berendsen Far Hills Country Day School Far Hills, NJ ------------------------ Nathaniel Stein Ms. Miller's 3rd Grade Schofield School Wellesley, MA ------------------------ Mike M. Grade 3, Ms. Seager Bagnall School Groveland, MA ------------------------ Alexander Salhany Mrs. Trudell's 3rd Grade Center School Stow, MA ------------------------ Scott Sacra Mrs. Trudell's 3rd Grade Center School Stow, MA ------------------------ Connie, Jackie, Tom, Alex, Philip, Jason, & Russell Grade 3, Ms. Seager Bagnall School Groveland, MA ------------------------ Nate, Justin, Emily S., Emilyn, Brian P., Nathan, & Ariel Mr. Coulter's Grade 3 Math Class Forsyth School St. Louis, MO ------------------------ Mrs. Hanley's Grade 3 Math Class Gilead Hill School Hebron, CT ------------------------ Vinay Aggarwal Grade 4, Mr. Nass Georgetown Day School Washington, DC ------------------------ Eric Schaffer Grade 4, Mrs. Cote Lyncrest School Fairlawn, NJ ------------------------ Jeffrey & Patrick Grade 4, Ms. Seager Bagnall School Groveland, MA ------------------------ Keith & Andy Grade 4, Ms. Seager Bagnall School Groveland, MA ------------------------ David & Joey Grade 4, Ms. Seager Bagnall School Groveland, MA ------------------------ Caitlyn & Stephanie M. Grade 4, Ms. Seager Bagnall School Groveland, MA ------------------------ Sarah & Jessica Grade 4, Ms. Seager Bagnall School Groveland, MA ------------------------ Stephanie D., Bethie, & Alison Grade 4, Ms. Seager Bagnall School Groveland, MA ------------------------ Mrs. Brennan's Grade 4 Drexel Hill School of the Holy Child Drexel Hill, PA ------------------------ Grade Four Math Class Room 15 W.E. Balmer School ------------------------ Jessica Anderson 5th Grade, Mrs. Anderson Homeschool Atlanta, GA ------------------------ Mike 5th Grade, Ringler/Carter Three Oaks Elementary School Three Oaks, MI ------------------------ Jeni 5th Grade, Ringler/Carter Three Oaks Elementary School Three Oaks, MI ------------------------ Lisa Grade 5, Ms. Gerber Mitchell School Needham, MA ------------------------ Steven LeBlanc Grade 5, Mr. Latshaw Park Avenue Elementary School Freehold, NJ ------------------------ Josh Grade 5, Ringler/Carter Three Oaks Elementary School Three Oaks, MI ------------------------ Emily Grade 5, Ringler/Carter Three Oaks Elementary School Three Oaks, MI ------------------------ Margaret Grade 5, Ringler/Carter Three Oaks Elementary School Three Oaks, MI ------------------------ Megan Grade 5, Ringler/Carter Three Oaks Elementary School Three Oaks, MI ------------------------ Paul Grade 5, Ringler/Carter Three Oaks Elementary School Three Oaks, MI ------------------------ Mary Grade 5, Ringler/Carter Three Oaks Elementary School Three Oaks, MI ------------------------ James Grade 5, Ringler/Carter Three Oaks Elementary School Three Oaks, MI ------------------------ Sarah Bodeau 5th Grade, Mrs. Watkins Manz, ECASD Eau Claire, WI ------------------------ Sara A. Kiekhoefer 5th Grade, Mrs. Watkins Manz, ECASD Eau Claire, WI ------------------------ Michael Clark Mrs. Freeman's Grade 5 Stony Lane School North Kingstown, RI ------------------------ Matthew Magliocco & Willy Smith Grade 5, Mrs. Lynagh & Mr. Schuman Collegiate School New York, NY ------------------------ Stephanie & Megan Mrs. Freeman's Grade 5 Stony Lake School North Kingstown, RI ------------------------ Megan & Sean Grade 5, Ms. Seager Bagnall School Groveland, MA ------------------------ Julia & Chris Grade 5, Ms. Seager Bagnall School Groveland, MA ------------------------ Laura & Alex Grade 5, Ms. Seager Bagnall School Groveland, MA ------------------------ Melissa, Matthew, & Darcy 5th Grade, Mrs. Hayes Shaffer Elementary Littleton, CO ------------------------ Jenny Rector, Mikyala Shea, & Caitlin Hinz 5th Grade, Mrs. Hamilton Garrison Elementary School Dover, NH ------------------------ Joshua, Christine, & Kyle Grade 5, Ms. Seager Bagnall School Groveland, MA ------------------------ Wayne Ting Form 3, Mr. Olver Macleans College Auckland, New Zealand ------------------------ Cody Moore Grade 6 Battleford Central School Saskatchewan, Canada ------------------------ David G. Grade 6, Ms. Lalumiere Bagnall School Groveland, MA ------------------------ Jen & Nicole Grade 6, Mrs. Caruso Bagnall School Groveland, MA ------------------------ Trevor & Art Grade 6, Mrs. Caruso Bagnall School Groveland, MA ------------------------ Lauren & Pam Grade 6, Mrs. Caruso Bagnall School Groveland, MA ------------------------ Chris & Brian B. Grade 6, Mrs. Caruso Bagnall School Groveland, MA ------------------------ Amanda & Leah H. Grade 6, Mrs. Caruso Bagnall School Groveland, MA ------------------------ Katelyn R. & Jessica Grade 6, Mrs. Caruso Bagnall School Groveland, MA ------------------------ Bryan C. & Katelyn E. Grade 6, Mrs. Caruso Bagnall School Groveland, MA ------------------------ Tom & Mike C. Grade 6, Mrs. Caruso Bagnall School Groveland, MA ------------------------ Regina, Lindsi, & Amy Grade 6, Mr. Crescitelli J.F.K. Middle School Northampton, MA ------------------------ Brendan Molaghan, Marlon Adams, & Eric LaValley Grade 6, Mr. Crescitelli J.F.K. Middle School Northampton, MA ------------------------ Elaina, Shawn, & Pat Grade 6, Mrs. Caruso Bagnall School Groveland, MA ------------------------ Peter, Sarah, & Nicole C. Grade 6, Mrs. Caruso Bagnall School Groveland, MA ------------------------ Alma Lincoln, Hannah Todd, Rebecca Straley, & Peter Boliver Grade 6, Mr. Crescitelli J.F.K. Middle School Northampton, MA ------------------------ Jill Smith Mrs. O'Connor Titus Elementary Warrington, PA ------------------------ Irish Duo W. Edward Balmer School Northbridge, MA ------------------------ Allison Wells & Kendra Berg Mrs. Watkins Class Manz Elementary Eau Claire, WI ------------------------ Bdyer123@aol.com
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