I had hired a worker to perform a job. He had to work for 15 days to finish my job. I was supposed to pay him with a fixed qualtity of gold every day. I had a long gold bar which had just enough gold to pay him for 15 days. (Assume that the bar was uniform throughout).
Now, I want to cut this bar only at 3 places and at the end of each day balances with each should be perfect.
For example, at the end of day 5, worker should have 5units of gold and I should have 10 units of gold. At the end of day 6, worker should have 7 6units of gold and I should have 8 units of gold.
Now any amount of interaction between the worker and me is allowed. (For example, I can take back a pice given to the worker yesterday and give him a new piece of gold today which covers all his wages to date.)
Now, where should I cut my bar assuming that it has 15 units marked on it?