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Cutting a Sausage into 11 (illustration)
FILE No.108Unsolved

Cutting a Sausage into 11

Difficulty ★☆☆about 5 minLogic PuzzleFence-post countingHow to count
A man asked for a sausage in 11 pieces and was cut 11 times, but got no payment. Why?

Case Record

An eccentric chef asked a young man, "Cut this sausage into 11 pieces. I'll pay you 1,000 yen." The young man made 11 cuts with a knife, one spot at a time. But the chef did not pay him a single yen.

Your question

Why not?

Case Files

Diagram

Cutting a sausage (example: 3 cuts)Each cut goes through one spot.The chef wants 11 pieces. The young man made 11 cuts.
Diagram

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

How many pieces after one cut?

Open hint 2

After two cuts?

Open hint 3

What is the relationship between cuts and pieces?

Solve It

Your question

Why not?

Choose the answer closest to the truth.

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The Truth

Because 11 cuts make 12 pieces

The answer is "Because 11 cuts make 12 pieces."

One cut makes a sausage 2 pieces, 2 cuts make 3 pieces, and so on. n cuts give (n + 1) pieces. Eleven cuts make 12 pieces, not 11.

You get 10 pieces after 9 cuts.

Number of cuts and piecesCutsPieces1223341011 ← what was ordered1112 ← what he maden cuts make n + 1 pieces.
Diagram of the solution

Key Points

  • Distinguish the number of cuts from the number of pieces
  • One cut gives 2 pieces, two cuts give 3
  • Same idea as fence-post counting

Why people get fooled

Because you match them directly: "11 pieces means 11 cuts."

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