You have some work to be done by a worker in 7 days. The worker need to be paid every day after his work. The total cost of the work of 7 days is one gold bar (so every day the worker must be paid 1/7’th of the bar).
You have only one gold bar, and you can make only two cuts in that bar. How will you ensure that the worker is paid every day?
If you think of somehow breaking the bar into 7 pieces then you are approaching the problem wrongly.
You have to break the gold bar in such a way that you can make transactions.
When we pay in money, then also it may be the case that we don’t have the change, so we give a bigger note to the worker and he return the change to us (for example, If we are supposed to pay Rs. 80, we give a Rs. 100 note to the worker and he returns Rs. 20)
We have to apply the same thought process here…
Make the two cuts in the bar in such a way that we have following three pieces of the gold bar:
- 1/7 —- Bar-A
- 2/7 —- Bar-B
- 4/7 —- Bar-C
Give Bar-A to worker (You have Bar-B and Bar-C, Worker has Bar-A)
Give Bar-B to worker and take Bar-A back (You have Bar-A and Bar-C, Worker has Bar-B)
Give Bar-A to the worker (You have Bar-C, Worker has Bar-A and Bar-B)
Give Bar-C to the worker and take back Bar-A and Bar-B (You have Bar-A and Bar-B, Worker has Bar-C)
Give Bar-A to worker (You have Bar-B, Worker has Bar-A and Bar-C)
Give Bar-B to worker and take back Bar-A (You have Bar-A, Worker has Bar-B and Bar-C)
Give Bar A to worker (You have nothing and all the bars are with worker)
Hence, you are able to pay the worker on daily basis and at the end the entire gold is with the worker.