Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits $1$ to $9$ each once and only once.

The number $4396$ can be written as just such a product. Can you find the factors?

Maths is full of surprises! The number $5796$ can be written as a product like this in two DIFFERENT ways, and so can the number $5346$. Can you find these four funny factorisations?

Here is another puzzle, again you must use the digits $1$ to $9$ once, but only once, to replace the stars and complete this multiplication example.

	*	*	$9$
		$4$	*
---	---	---	---
*	$6$	*	*

This gives altogether six funny factorisations and there is one more. You might like to write a computer program to find all seven funny factorisations or you might come up with a different method. Let us know.