The market scales puzzle & connections with ancient Egyptian mathematics: Homework for Monday Sept 28

 Here's a puzzle that connects with the principles of ancient Egyptian multiplication in interesting ways. There's a story connected with this puzzle that I'll tell you in class -- but here's the puzzle:

A market vendor sells dried cooking herbs in whole-number amounts from 1 to 40 grams. The vendor has an old-fashioned two pan weigh scale, and has exactly four weights of different amounts that allows them to weigh out any of these amounts of herbs -- without using the herbs or any other object as an auxiliary weight.

• Make sure you understand how a two-pan scale works...the weights can be placed on either or both of the pans.
  
  
• What must the values of the four weights be? Why?
  
  
• What if it was a one-pan scale -- i.e., a scale where you could only put the weights on one of the pans, rather than both of them? What five weights would you need to weigh up to, say, 31grams?
  
  
• How could you extend this puzzle to help your students understand the mathematics more deeply?
  
  
• How does this puzzle connect with ideas about number theory and bases you are already familiar with?
  
  
  

Please post your blog on this problem next  Monday September 28 by 9 AM.

Enjoy!

Dave Wagner: two-pan market scales, Bhutan. Used with permission.