Things and the gaps between them

The question

A log is sawn into 15 equal pieces.

How many cuts does that take?

The things, or the gaps between them

pieces:15
pieces:15
●—●—●—●
14
  1. Here is what the question gives.
  2. The numbers give you one count straight away: 15 pieces — but is that the answer?
  3. Look at a small row — four dots have three gaps. Whether you add one depends on what is at the ends.
  4. Cuts sit between the pieces, not at the ends: 15 pieces have 15 − 1 = 14 cuts. Break a stick in two and you cut once.

How it works.

  1. 01

    Here is what the question gives.

  2. 02

    The numbers give you one count straight away: 15 pieces — but is that the answer?

  3. 03

    Look at a small row — four dots have three gaps. Whether you add one depends on what is at the ends.

  4. 04

    Cuts sit between the pieces, not at the ends: 15 pieces have 15 − 1 = 14 cuts. Break a stick in two and you cut once.