The following problem was offered to me a few years ago by John Hinton of Math Matters Inc. I plan to let my students struggle with this problem for a few days before I give them hints. The problem stretches the students' abilities to analyze the patterns that exist in divisibility.
I hope you and your students have fun struggling with this problem, as well. As you work with the problem, please send suggestions or questions that have come up in your classroom.
How many counting numbers between 10,000 and 100,000 are divisible by nine of the following ten numbers: