Dust Wars

When their parents die in a tragic accident, daughters Joan and Marie read their parents' Last Will and Testament. The Will is very short, because there is only one asset: two kilograms of gold dust.

The Will states that Joan, as the elder sister, should divide the dust into two piles: we will call those piles A and B. Then she is to cut pile A into two smaller piles that we will call A1 and A2. Marie can decide to choose one of A1 or A2 or not. If Marie chooses, then Joan takes the other smaller pile and all of pile B. If Marie does not choose between A1 and A2, then Joan can choose one of them (presumably the larger one) and give Marie the other one and then Joan must cut pile B into B1 and B2 and Marie can choose which one she wants.