Puzzle | Minimum cut Puzzle
Last Updated :
19 Aug, 2025
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You hire a worker for 5 days and agree to pay them 1 unit of gold at the end of each day. However, you only have a single 5-unit gold bar.
The conditions are:
- The worker must be paid exactly 1 unit per day.
- You are allowed to cut the gold bar into pieces.
- After cutting, you can use those pieces to make exact payments each day.
What is the minimum number of cuts required to split the gold bar so that you can pay the worker correctly for all 5 days?
Check if you were right - full answer with solution below.
Answer: 2 cuts
Solution:
- Start with a 5-unit gold bar.
- Cut 1: Make the first cut at the 1-unit mark- gives 1 unit and 4 units remaining.
- Cut 2: Cut the 4-unit piece in half, giving two 2-unit pieces.
- Final pieces: 1 unit, 2 units, 2 units
It can also be explained using the table below:
| Days | Worker Gets | Vendor Takes Back | Worker Holds | Explanation |
|---|---|---|---|---|
| Day 0 | - | - | [] | No Payment yet. |
| Day 1 | [+1] | - | [1] | Pay the worker Gold Bar with 1 unit. |
| Day 2 | [+2] | [-1] | [2] | Pay the worker Gold with 2 units and take back the gold bar with 1 unit. |
| Day 3 | [+1] | - | [1,2] | Pay the worker Gold Bar with 1 unit. |
| Day 4 | [+2] | [-1] | [2,2] | Pay the worker Gold with 2 units and take back the gold bar with 1 unit. |
| Day 5 | [+1] | - | [1,2,2] | Pay the worker with only left Gold Bar with 1 unit. |
Therefore, by making just 2 cuts, you obtain 1-unit, 2-unit, and 2-unit gold pieces, which allow you to pay exactly 1 unit per day over 5 days through a combination of giving and taking back pieces.
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