# Framed Numbers

one

two

three

four

five

one

one

one

one

one

two

two

two

two

three

three

three

four

four

five

### 💥 TRY AGAIN 💥

That's not the solution required.

Figure out which numbers will complete the sentences in the frame correctly

## A Mathematics Lesson Starter Of The Day

Topics: Starter | Problem Solving | Puzzles

• Transum,
• Friday, August 23, 2024
• This puzzle is the Transum version of those known as self-referential sentence puzzles or sometimes a self-descriptive sentences.

The origins of these kinds of puzzles are not definitively attributed to a single person, but they have been popularized by recreational mathematicians over the years. One of the earliest mentions of such self-referential puzzles can be found in works by American mathematician and logician Raymond Smullyan, known for his books on logic puzzles, paradoxes, and self-reference.

Another key figure associated with self-referential puzzles is Douglas Hofstadter, an American professor of cognitive science, who explored self-reference and paradoxes in his influential book GĂ¶del, Escher, Bach: An Eternal Golden Braid (1979).

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

Previous Day | This starter is for 24 August | Next Day

## Clue

So you're students are finding it too difficult? Click the button below to take away the distractors so that you will only be left with the five solutions which need to be placed correctly.

## Extension

Consider a frame containing only the first four sentences. There are two different solutions to that problem, can you find them both?

Is it possible to find a solution to a frame that contains six such sentences?

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