Elementary POW, January 20-24, 1997
Elem POW Problems || Dec '96 - Feb '97 Problems || Elem POW Main Page
The diagram shows the numbers 1 through 10 (in order) at the tips of 5 diameters. Only once does the sum of two adjacent numbers equal the sum of the opposite two numbers:
Elsewhere, for example,
Rearrange the numbers so that all sums are equal. You can expect more than one solution to this problem. How many basic solutions are there? (Do not include simple rotations of the same numbers - for example 1,2,3,4,5,6,7,8,9,10 would be the same as 2,3,4,5,6,7,8,9,10,1.)
This week's mentor is Jackie Roth, Grade 9, Germantown Academy, Fort Washington PA.
Casey Gorish (Almost all correct) 6th grade Mrs. McMahon Murray Middle School Ridgecrest Ca Bobby Blanton, Joshua DeBenedetto,Ted Powers, Timothy Bolton Grade 4 - Miss McGuire, Center School - Stow MA Alex Smith Grade 5 Teachers: Anne Lynagh, Paul Schuman csms5@interport.net Collegiate School, New York, NY Peter Canter Grade 5 Teachers: Anne Lynagh, Paul Schuman csms5@interport.net Collegiate School, New York, NY Forsyth School Third Grade Bob Coulter Individual solutions by: Brian Powers, Sarah Haspiel, Nate Litz, Nathan Strauss, Justin Weiss, Rosemary Forsyth. Nick Lane Mr. Granger's Fifth Grade Class Marysville, WA Lizzie Crow Brendan Feinberg, grade 2 Sam Henderson, grade 5 Jessi Soler and Rachel Licht, grade 3 Andrew Dang, grade 5 Western Salisbury School (Mrs. Geschel) Allentown, PA 18103 Mark Trama's 3rd Grade Class Ithan Elementary School, Bryn Mawr, PA E-Mail: mtrama@itrc.dciu.k12.pa.us We all worked on our own at home and between us generated 8 different solutions: Mike, Marina, Jim, George, Peter, Scott C., Claire : Scott P., Robby: Yiqiong: Eric: Gi-Soo: Katie: Samantha: Nathaniel Stein Heather Miller, teacher Schofield School Wellesley, MA Sean Mayo Grade 5 Mrs. Hamilton's Garrison School in Dover, N.H. Allan Salter and Chris Briggs Grade: 5th/6th Teacher's Name: Kari Williams School: Idaho Hill Elementary Location: Oldtown, Idaho Andrew RichardsonMrs. Davis's 4th Grade Asheville Christian Academy Asheville, NCE-mail: ldavis@montreat.edu Katie, Lauren, Claire, Daina, Steve and Tim Grade 4 Mrs. Brennan Drexel Hill School of the Holy Child Drexel Hill, PA Jennifer 4th Grade Stony Lane School North Kingstown, RI Greg 3rd grade Jackson St.Paul MN 4th and 6th grade students Mrs. Hayes Shaffer Elementary Littleton CO Bryan C. and Peter M. Grade 6 Mrs. Caruso Bagnall School, Groveland, MA Katelyn R. and Curt D. Grade 6 Mrs. Caruso Bagnall School, Groveland, MA Elyse D. Grade 5 Mrs. Crawford Bagnall School, Groveland, MA Meghan Ramsey Grade 5 Mrs. Crawford Bagnall School, Groveland, MA Meaghan Carroll Grade 5 Mrs. Crawford Bagnall School, Groveland, MA Alex, Russell, Jason, Connie, Philip Grade 3 Miss Seager Bagnall School, Groveland, MA Alison, Caitlyn, Jessica, Sarah, Stephanie, Jeffrey, Keith, and Joey, Grade 4, Miss Seager Bagnall School, Groveland, MA Elizabeth Clark, Lydia Nations, and Addie Small Carroll Intermediate School ,Carroll I.S.D. 6th grade 1101 N. Carroll Ave., Southlake, TX 76092 Teacher - Mrs. S. Dedek Erik and Dom Grade 3 Monfort Elementary Greeley, CO
Hello,From the top mark on the circle (normally 0 degrees), these numbers are:
4, 5, 8, 9, 2, 3, 6, 7, 10, 1
However, the area on the circle where you begin shouldn't matter (i.e. you could use the 72 degree mark for the 4, the 108 degree mark for the five, and so on).
>You can expect more than one solution to this problem. How many basic >solutions are there?
I've tried a couple of ways and have no idea how many there are. That's a tough problem.
I am a sixth grader at The Prairie School in Racine, WI.
Victor Osimitz
Mark Trama's 3rd Grade Class
Ithan Elementary School, Bryn Mawr, PA
E-Mail: mtrama@itrc.dciu.k12.pa.usWe all worked on our own at home and between us generated 8 different solutions:
- Mike, Marina, Jim, George, Peter, Scott C., Claire :
6, 2, 8, 4, 10, 1, 7, 3, 9, 5 - Scott P., Robby: 9, 2, 10, 1, 8, 4, 7, 5, 6, 3
- Yiqiong: 10, 2, 8, 1, 9, 5, 7, 3, 6, 4
- Eric: 10, 1, 8, 3, 6, 9, 2, 7, 4, 5
- Gi-Soo: 10, 1, 9, 2, 8, 5, 6, 4, 7, 3
- Katie:10, 1, 8, 2, 9, 5, 6, 3, 7, 4
- Samantha: 10, 7, 6, 1, 4, 9, 8, 5, 2, 3
And lastly, Claire arranged the numbers a second way also -
10, 1, 9, 3, 7, 5, 6, 4, 8, 2 - She had the 10 and 1 at the top of the circle and the 5 and 6 at the bottom. She had one of those "a-ha" moments when she discovered that if you write the differences between neighboring numbers in the space between the numbers, that these differences show a symmetry. For example, 6 and 5 are neighboring numbers and their difference is 1. When you head out 1 spot in each direction, the 6 and 4 are neighbors and the 5 and 7 are neighbors - they each have a difference of 2. The 8 and 4 and the 7 and 3 each have a difference of 4. The differences go up each side from the bottom 1, 2, 4, 6, 8, and then lastly, 9 at the top between the 10 and the 1.
[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.
