Puzzle 31 | (Minimum cut Puzzle)

Puzzle: You have got someone working for you for five days and a gold bar to pay him. You must give them a piece of gold at the end of every day. What are the fewest number of cuts to the bar of gold that will allow you to pay him 1/5th each day?

 

 

 

 



Answer: 2 cuts.

Solution:

Explanation 1:

After two cut there are three pieces of [1 unit and two 2 units] or [two 1 units and one 3 unit]. Now perform the following transactions.

[1 unit and two 2 units]

Days Gold Bars(Vendor) Gold Bars(Worker) Comments
Day 0 [1, 2, 2] [] Intially Worker have 0 Gold Bars unit.
Day 1 [2, 2] [1] Pay the worker Gold Bar with 1 unit.
Day 2 [1, 2] [2] Pay the worker Gold with 2 units and take back the gold bar with 1 unit.
Day 3 [2] [1, 2] Pay the worker Gold Bar with 1 unit.
Day 4 [1] [2, 2] Pay the worker Gold with 2 units and take back the gold bar with 1 unit.
Day 5 [] [1, 2, 2] Pay the worker with only left Gold Bar with 1 unit.

[two 1 units and one 3 unit]

Days Gold Bars(Vendor) Gold Bars(Worker) Comments
Day 0 [1, 1, 3] [] Intially Worker have 0 Gold Bars unit.
Day 1 [1, 3] [1] Pay the worker Gold Bar with 1 unit.
Day 2 [3] [1,1] Pay the worker Gold with other 1 units.
Day 3 [1,1] [3] Pay the worker Gold Bar with 3 unit and take back all the gold bar with 1 unit.
Day 4 [1] [1, 3] Pay the worker Gold with 1 unit.
Day 5 [] [1, 1, 3] Pay the worker with only left Gold Bar with 1 unit.

Similar Puzzle: Pay an employee using a 7 units gold rod?

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