Egyptian geometry and other challenges: Let’s play math!

Egyptian geometry and other challenges: Let’s play math!:

Here is a math “magic trick” from the Rhind papyrus. (Warning: The Egyptian scribes loved working with fractions.) Your job is to explain why it works. How could Scribe Ahmose know that he would always be able to tell what number his friend had in mind?

• Tell your friend to think of a secret number. [To avoid fractions, pick a multiple of 9.]
  
• Then have him add 2/3 more to his number. [So if he started with 9, he would add 2/3 of 9: 9 6 = 15.]
  
• Finally, tell him to take away 1/3 of this total, and say the answer. [1/3 of 15 is 5, and 15 - 5 = 10.
  
• Your friend would say, “Ten.”]
  
• Now you must subtract 1/10 of that number to find the secret. [1/10 of 10 is 1, so the secret number is 10 - 1 = 9.]
  

OK, here is my algebraic solution: (x is the chosen number):

TA DA! 

I enjoy showing these (but simpler ones) to my college algebra classes. Usually the students enjoy it too and look for other math tricks to solve. Denise has posted the answers. This is my 2nd puzzle to solve. I want to do the triangle one before I peek at the solutions. I hardly ever teach geometry, so I want to look up the triangle inequality thing before I start. 

When clicked, this jpeg will open, full size, in a new window. This would've been more easily understood as a "paper" entry (papyrus / paper) for this week's photohunt instead of my Frost poem, which seemed to confuse people. Too late now.

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