Problem 2. Dragan, Bobi, and Martin together have 12000 denars. Dragan divided half of his money into two equal parts and gave them to Bobi and Martin, and kept the other half for himself. Bobi did the same,

and then Martin, after which the three friends had the same amount, i.e., 4000 denars each. How much money did each of them have at the beginning?
Solution. Let's not start solving the problem in reverse. At the end of the divisions of the money, they all had the same amount, namely 4000 denars. Before the division of the money, Martin had $4000 \cdot 2=8000$ denars, and Dragan and Bobi had $4000-4000: 2=2000$ denars. Before Bobi divided his share as described in the problem, he had $2000 \cdot 2=4000$, and Dragan and Martin had $2000-2000: 2=1000$ and $8000-2000: 2=7000$ denars, respectively. Finally, at the beginning, Dragan had $1000 \cdot 2=2000$ denars, Bobi had $4000-1000: 2=3500$ denars, and Martin had $7000-1000: 2=6500$ denars.