I ran across a nice mathematical puzzle recently. It’s called “Nob’s Number Puzzle”. Here it is:

The answer is given at the bottom of this post. The puzzle is clever but not some sort of crazy thing: you should be able to find the missing number with a bit of thought.

“Nob” is the nickname for Nobuyuki Yoshigahara (1936–2004) a well-known puzzle creator.

I remember taking tests when I was young that contained questions where the goal is to find the next number in a sequence. For example, 1, 1, 2, 3, 5, 8, 13, 21, ? is the Fibonacci sequence where each number is the sum of the previous two numbers, so the missing number is 13 + 21 = 34.

One of my favorite missing number puzzles is: 1, 4, 9, 7, 7, 9, 4, 1, ?

The sequence is 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16 = 7, 5^2 = 25 = 7, 6^2 = 36 = 9, 7^2 = 49 = 13 = 4, and so on. You square each integer in order and if the result is more than one digit, you add the digits. So the missing number is 9^2 = 81 = 9.

Knowing this squared-number puzzle was the reason I was able to solve Nob’s number puzzle quickly. That is a hint for Nob’s puzzle.

Years ago, puzzle questions like these were very common in job interviews at places like Microsoft and Google. I never liked puzzle questions for job interviews and I never used them. My go-to question in a job interview is “Tell me about a project or hobby you’ve done in your spare time that you’re proud of.”

For example, if I were asked this question in an interview, I’d tell the interviewer about my Zoltar program that predicts the results of NFL professional football games.

When I ask a job candidate this question in a job interview, one of two things usually happens.

First, a candidate can come up with an answer quickly and get very excited to tell me about their project in great detail. In general, I am impressed with a guy like this. The exact project doesn’t matter as much as the passion I see in him.

Second, a candidate doesn’t come up with a hobby-project or tells me about a school assignment. This isn’t a deal-killer but I’m not impressed and continue the interview with additional questions to see if the candidate has a true love of programming and software development, or if he is just looking for a job.

Answer to Nob’s number puzzle: the missing number is 12. On the top row, 7 + 2 + 9 + 9 = 27. Second row, 2 + 7 + 4 + 5 = 18. And so on. Simple and elegant!

Notice that if the numbers were written as 7 2, 9 9 instead of 72, 99, the puzzle would be much easier to solve.

Three puzzle boxes. The goal is to open the box. Puzzle boxes range from simple and easy to sophisticated and almost impossible to solve.