Elementary POW, May 5-9, 1997
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The sectors (slices) of this circle all follow a pattern. Describe the pattern, and tell what three numbers belong where the question marks are.
This week's mentors are Stuart Wyss and his 30 math students at the Paul W. Kutz Elementary School, who write:
The correct answer is any three single-digit numbers that add up to 11, since opposite sectors are equal to each other. Congratulations to everyone who solved it!
Chris England, John England, and Eric Austin Phoenix Country Day School Vinay Aggarwal Georgetown Day School, Washington DC Brett S. Mission Meadows Elementary, Oceanside, CA Adam Litterman & Co. Millburn Middle School, Millburn, NJ Nicole Vanlengen Countryside Elementary School, Terr. Olathe, KS William Ewing Center School, Stow, MA Blaire Johnson Battleford Central School, Battleford, SK, Canada (our only non-US response. Thanks!) Alex Abrams Underwood School, (no city or state given) Melissa Griffith Underwood School, (no city or state given) Tyler Bryan Manz, ECASD, Eau Claire, WI Ashley, Amy, Kali, Mariah, Mike, Sara, Kerry, Katie, and David Bagnall School, Groveland, MA Brad Gorg Titus Elementary School, Warrington, PA Lizbeth Martinez H.D. Hilley School, El Paso, TX Catie Cosgrove Countryside Elementary School, Olathe, KS Joe Bauer and Zach Paulson Manz, ECASD, Eau Claire, WI Miguel Diaz H.D. Hilley School, El Paso, TX Josh Smith, Tom Hayes, and Ryan Schwartz Kutz Elementary School, Doylestown, PA Michael Hajatian, Billy Hackett, and Andrew Jones Kutz Elementary School, Doylestown, PA Zack Seibert Western Salisbury School, Allentown, PA Edwardo Chavez H.D. Hilley School, El Paso, TX Nydia Aleman H.D. Hilley School, El Paso, TX Willie Moya H.D. Hilley School, El Paso, TX Diane Rubalcava H.D. Hilley School, El Paso, TX Andrew Markquart Manz, ECASD, Eau Claire, WI Pat & Jeff, Caitlyn, Stephanie M. & Alison, Stephanie D. & Bethie, Keith & David, Sarah & Jessica, and Andrew & Joey Bagnall School, Groveland, MA Jammie, Kelly, & Beth Manz, ECASD, Eau Claire, WI Mrs. Gleichman's Sixth Grade Class Grace Russell Elementary School, Wilburton, OK Libbie Watkins Manz, ECASD, Eau Claire, WI Michael Pontiff Manz, ECASD, Eau Claire, WI Paul S. Gorish (no school given) Ridgecrest, CA Jim and Jimmy (no info given) Erika Guzman H.D. Hilley, El Paso, TX Chris Lange Manz, ECASD, Eau Claire, WI Christy Hernandez H.D. Hilley School, El Paso, TX Ryan Sperbeck Emerson Elementary, Madison, WI Cassie, Alex, Lisa, Mike, Phil & Catherine, Dan, Roman, Jessica, Molly, & Mike W., Justin, Jeff, Anne, Alise, & Maggie, Dave, Pete, Kim, Neil, & Jake, Mitchell School, Needham, MA Rick Jacobs (no info given) Ryan Seeley Manz, ECASD, Eau Claire, WI
Special recognition goes to Ms. Julie Thomsen's 3rd/4th multi-age class at East Ward Elementary School, McCook, Nebraska.Answer: After examining the sectors of the circle and exploring the possibilities using comparison, addition, subtraction, and moving clockwise and counter-clockwise as well as across the circle, we could see only a limited number of possible solutions. First of all, the opposite sectors both have the same sum when the numbers in each are added. Therefore, the sum of the numbers in the sector with the question marks should be 11. Because there are no numbers larger than 9 anywhere else in the circle, we decided that the numbers that belong where the question marks are could be any of these:
9,1,1
6,2,3
5,1,5
5,2,4
5,3,3
5,4,2
4,3,4
9,0,2
8,0,3
8,1,2
7,0,4
7,1,3
7,2,2
6,0,5
6,1,4Also special commendation to Nicko Margolies, of Georgetown Day School, Washington DC. He wrote
First I looked at the inner and outer circles inside the big circle for a pattern. I tried to see if the pattern was adding, subtracting, multiplying,or dividing. I did this for the inner and outer circles. I never found a pattern. I then remembered that Mr. Wyss and his thirty students said to use the slices, so I added up all the digits in a slice. I then looked across the slice that I just added up and got the same thing. I then did what I just said with the slice across from the question marks. Therefore, I think the answer is nine, one, and one.
Congratulations again to everyone who submitted an answer. Without all of you, this would not be possible.
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