Three students, A, B, and C, each threw five marbles, which came to rest as shown. In this game, the winner is the student with the smallest scattering of marbles. The degree of scattering seems to decrease in the order A, B, C. Devise as many ways as you can to express numerically the degree of scattering. (From Becker and Shimada.)
sum of distances between all pairs of marbles
largest distance between a pair of marbles
radius of smallest circle containing them all
divide region into 10 equal regions and count number of marbles in each region
lay on increasingly fine grid until no two are in same region.
What if two are touching?
difficulties with widths of marbles
Does it matter? Can you set up two situations that would be compared differently if centers and outsides of marbles are measured?
Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!
Last updated 30 November, 2004