High School Challenge




|| Toothpicks ||


Using an 8.5 by 11 or larger sheet of paper and a toothpick, draw a series of parallel straight line segments that are a toothpick length apart (the length of the toothpick is the perpendicular distance between each two line segments).

Hold several toothpicks 2 to 3 feet above the center of the paper and drop them. A toothpick is ON if it touches one of the line segments (or, resting on another toothpick projects over a line segment) and OFF if it does not touch a line segment. A toothpick that bounces off the paper should not be counted. Repeat the process until the ONs plus the OFFs total 100.

What is the decimal value for twice the number of ONs divided by the number of OFFs? This activity was developed in 1760. Give the name of the principle you just showed.

From Brumbaugh, Ashe, Ashe, & Rock. (1997). "Teaching Secondary Mathematics", Lawrence Erlbaum Associates, Inc., Mahwah, NJ 07430-2262 (800-926-6579), page 173.


Correct Solutions:


  1. Adam Maberry. Buchannan ES, Pierre, SD
  2. Michael Gough. Walkersville HS, Walkersville, MD
  3. Russ Campbell. East HS, Columbus, IN
  4. Michael Franks. Merritt Island HS, Merritt Island, FL
  5. David Trocki. Columbus East HS, Columbus, IN
  6. Kolade Apata. B.E. Mays HS, Atlanta, GA
  7. Russ Campbell. East HS, Columbus, IN
  8. Tara Goodfellow. Seabreeze HS, Daytona Beach, FL
  9. Andy Coleman. Center for Arts & Sciences, Saginaw, MI
  10. Michael Franks. Merritt Island HS, Merritt Island, FL
  11. Nirmal Mankani. Center for Arts & Sciences, Saginaw MI
  12. Mike Bonifacius. Columbus East HS, Columbus, IN
  13. Justin Lam. College Park HS, Pleasant Hill, CA