Headline Story
The Eraser Store, #2
Click to enlarge
Introduction
Share the Headline Story with the class. Encourage students to think of creative ways to solve the problem.
Headline Story
There are 8 similar coins on a table. Seven have the same weight. The remaining one is lighter. How can we find out which coin is lighter using only a balance scale without weights?
Possible student responses
- We can compare two coins on the scale. If their weights are different, we’ve found the lighter one. If their weights are equal, we can compare one of them with each remaining ones, until we find the light one. This method requires is to use the scales at least once, at most 7 times.
- There is another way: we could compare the weights of any 4 coins with the 4 others. The lighter coin will be in the lighter group. We could then repeat the process comparing 2 coins from the lighter group with the other 2. Finally, we could compare the weights of the 2 coins in the lighter group from the previous weighing. This method guarantees that we will find the lighter coin using the scales exactly 3 times. Can we use scales only twice to find which coin is lighter?
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.