median
don steward
mathematics teaching 10 ~ 16

## Thursday, 30 April 2009

### Ben's game (not the video game about fighting cancer)

this problem is on the NRich site where there are detailed teaching notes

unfortunately their version only has one solution, so once students have found this solution they need something else to do...

the version here is slightly older (due to Diophantus ~ 200 CE) and has three solutions

Albert, Bella and Camus have a little problem
they don't know how much money they have each but do know it totals less than £50

Albert is going to give a third of their money to Bella
Bella is going to give a quarter of their money to Camus
Camus is going to give a fifth of their money to Albert

they are all going to pass on these fractions before they receive money from another person
they pass on their money all at the same time - all the transactions are simultaneous
so the fractions they pass on are of their original amounts

what they want to happen is that after they have passed on their money,
each will have the same amount of money

what amounts would they need to have to start with for this to happen?
what is the simplest solution?