Problem 2 · Pieces vs. cuts · 3 points
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A rope 12 m long is cut into pieces that are each 2 m long. How many cuts are needed?
- 4
- 7
- 6
- 5
- 3
Show a hint
- Try a smaller rope first. Start with one piece, make a cut, and notice how the number of pieces changes.
- Work out how many 2 m pieces the rope must become. Use the pattern from your smaller example to find the cuts needed.
Show the answer and solution
Answer: D — 5
The rope makes 12 ÷ 2 = 6 pieces. It starts as one piece, and each cut increases the number of pieces by one. So reaching 6 pieces takes 5 cuts. The answer is 5. Choosing 6 would mean counting one cut for every piece, but the last piece is already separated after the fifth cut.