Math PicnicEvery sheet is a promise

Always, sometimes, never, step by step

A claim about numbers is made, and the question is whether it holds every time, some of the time, or none of the time.

Practice Practice sheetNew questions
The question

An odd number times an even number is odd.

An odd number times an even number is odd.

An odd number times an even number is odd.
alwayssometimesnever
alwayssometimesnever
never
  1. Before trying anything, notice what each answer would COST. One example that works proves nothing at all. One that fails rules out "always" on its own. They are not the same size of evidence.
  2. So hunt for a counter-example — a case where the claim breaks. That is the cheapest question to ask, and its answer decides between all three.
  3. Try 13 and 28 — it fails, and so does every other case. So the answer is never.

How it works.

  1. 01

    Before trying anything, notice what each answer would COST. One example that works proves nothing at all. One that fails rules out "always" on its own. They are not the same size of evidence.

  2. 02

    So hunt for a counter-example — a case where the claim breaks. That is the cheapest question to ask, and its answer decides between all three.

  3. 03

    Try 13 and 28 — it fails, and so does every other case. So the answer is never.

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