Mathematics Problem Of the Week

Fall 2006

POW #10

Fair Shares

Albert, Lucy and Cuthbert have 11 full jars of oil, 11 jars half-full of oil and 11 empty jars. They want to share them so that each person gets the same number of jars and each person gets the same amount of oil.

How many inequivalent ways can they do this, assuming all the jars are sealed? Two ways are inequivalent if they contain different distributions of full, half-empty and empty jars. Once the division is made, we don't mind which pile Albert takes as they are all of equal value.

Can you generalize to the case of more (or fewer) jars?

Due Friday, December 1^st at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math office or sent via e-mail to rlock@stlawu.edu.