While attending a conference and hanging out with a college later in the day he recounted to me a nice mathematical puzzle that he learned while growing up in Algeria.
Three brothers were in a bind, they could not divide their father’s inheritance. Their father has left them with 17 camels and instructions that half of his camels should go to eldest son, a third to the second eldest, and a ninth to the youngest. Knowing that there is no point in having a fraction of camel, they wanted a solution that would be fair and yet that would result in no fractional division of camels. A passerby, seeing their predicament proposed to help.
In order to resolve their problem he donated his camel to the pool of 17 camels, bring thus the total to 18. One brother will hence get 9 camels, the other would get 6, and the youngest would get 2 camels. But 9+6+2=17, therefore the passerby concluded that he would walk away with the left over camel. Problem solved… but how?
Two farmers decided to sit down and share their lunch food. One farmer had on him five loafs of bread and the other had seven loafs. Just as they were about to start, a passerby asked if he could join them. The three sat down and they equally divided the twelve loafs amongst themselves. When they were done, the passerby give them twelve dirhams for the meal. The farmer who contributed five loafs proposed that a fair division of that amount would be for him to take five dirhams and for the other farmer to take the remaining seven. A disagreement ensued. They sought the assistance of judge to resolve their disupte and his resolution was that the farmer who contributed five loafs should only walk away with three dirhams, while the other should have the remaining nine dirhams. How is this fair?