Brain Teaser 30: Division by 9
Hi, I’ve developed a keen interest in brain teasers lately and thought, why not share and discuss them here. These brain teasers could potentially be asked during interviews for quantitative-related roles. They are taken from the book ‘A Practical Guide to Quantitative Finance Interviews’ by Xinfeng Zhou. The problem that we’re gonna solve in this post is “Division by 9”.
Problem:
Given an arbitrary integer, come up with a rule to decide whether it is divisible by 9 and prove it.
Solution:
A nice property that multiples of 9 has is that the sum of all the digits is also divisible by 9.
Therefore, given an arbitrary integer, sum up the digits. If the sum is divisible by 9, then the given integer is divisible by 9; otherwise, the given integer is not divisible by 9.
Proof:
And that’s all for this brain teaser about division by 9️⃣. Any feedback or questions are welcome! Are you interested in more brain teasers 🧠? Check out the other problems in this series:
Thank you for reading! :)
