Why do this problem?
This problem helps students to appreciate the power of algebra for solving problems involving number and place value. It would make a good follow-up problem for students who have worked on Reversals
This printable worksheet may be useful: Puzzling Place Value
You may wish to use this problem for consolidation in class or homework, after working on Reversals
or Always a Multiple
When students have had a go at tackling the questions, take some time to discuss the answers as a class, focussing particularly on their explanations of why there were only a limited number of solutions, or why the solutions they have found satisfied a particular condition.
Is there an algebraic expression to represent the problem?
Are there any restrictions on A, B and C?
For students who are ready to explore algebraic representations with quadratic expressions, Factorising with Multilink
and Pair Products
may be suitable follow-up problems.
Always a Multiple
offers multiple representations for solving place value problems, so it might be a good problem to try before looking at this one.