This prompt appears in Boris Kordemsky's The Moscow Puzzles (1956), in which Kordemsky lists the full set of equations of this type. As students invariably observe in the first phase of the inquiry, there are two key features of the equation (or 'rules') - the numbers are 'doubled and halved' and the digits are 'reversed'.
Once students have assured themselves that the equation is correct, they are enthusiastic to find more examples of the same type. The inquiry, therefore, is ideal for developing students' fluency with multiplication in the wider context of answering their own questions, testing their own conjectures and reaching aims they helped to establish.
As the inquiry develops, the teacher can guide the class towards using - or co-construct in a class discussion - an algorithm to generate more examples (see below in 'Notes'). Overall, the prompt offers a wealth of possible pathways that have the potential to combine multiplication, algebra of the form (10a + b)(10c + d) = (10b + a)(10d + c), and substitution with the concepts of ratio, prime factors, and algorithms.
This prompt, along with four others, was developed with the assistance of a Gatsby Teacher Fellowship in 2004-05. Details are available here. I am grateful to the Gatsby Educational Trust for the interest it showed in my early work at a time when inquiry teaching seemed out-of-step with the orthodoxy of the National Numeracy Strategy. Guided poster Devised by Emma Morgan, a maths teacher, to guide students when presenting their inquiry. Emma blogs here about using Inquiry Maths. You can read more examples of how this inquiry has developed in the classroom in the primary section of the website.