Why do this problem?
is a quirky puzzle that gives students an opportunity to express algebraically what is known in order to deduce relationships. It is a nice example of a problem that can be solved using algebra but also by finding a neat way to think about the situation.
This problem could follow on from work on What's it Worth?
Once students have had a chance to think about the problem, take some time to discuss solution methods. One neat way to think about the problem is to realise that passing on three gems and receiving three different gems back leaves each jeweller with one of each gem plus their original collection minus 4...
What does each jeweller start with?
What does each jeweller end up with?
What can you deduce, knowing that each jeweller ends up with the same?
gives a challenging workout with lots of opportunity to practise simultaneous equations.
What's it Worth?
gives students an opportunity to think strategically about how to work out the value of unknowns.