Puzzle homework for Wed Oct 16: The Dishes Puzzle

   

From Wikimedia Commons:
Facsimile of Qing dynasty edition of
The Mathematical Classic of Sun Zi

"How many guests are there?" said the official.

"I don't know," said the cook, "but every 2 used a dish of rice, every 3 used a dish of broth, and every 4 used a dish of meat between them". There were 65 dishes in all. How many guests were there?

 A puzzle from 4th century CE, from the Sunzi Suan Jing 孙子算经 (China).

Reflection questions:

• How could you solve this puzzle without algebra (or at least, without the algebra we are used to)?

• Does it makes a difference to our students to offer examples, puzzles and histories of mathematics from diverse cultures (or from 'their' cultures!)

• Do the word problem or puzzle story and imagery matter? Do they make a difference to our enjoyment in solving it?

Please post your solution and reflections by Wednesday Oct 16 at 9 AM!