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    • Would you mind sharing your reasoning for how you got that?

      As a math educator, I’ve always been more interested in how students arrive at an answer than in whether they write down the correct answer. Maybe they’ve come up with an alternate solution to mine that also works. For my previous puzzle, there were at least two valid solutions discovered that were different from mine.

    • Sure - what I see before me is a sequence of all integers from 1 to 8 in random order. The only number missing from that sequence is 3, so 3 is the next number.

    • Nice thinking. I won’t say if your answer is correct or not because although the numbers appear randomly ordered, I can tell you that it is a non-random sequence and that there is a logic to the pattern. Shewmaker, based on his cleverly cryptic responses, has solved the riddle.

    • But why aren’t 3 and 9 part of the set?

      A sequence can skip items in a typical series. For example, what is the next number in these sequences:

      21, 22, 23, 25, 26, 27, 29, 30, ?

      A, B, C, E, F, G, I, J, ?

      January, February, March, May, June, July, September, October, ?

    • Sure, but why would you? To answer my own question (now I’ve thought about it more) it leaves the the puzzle intact. To have included 3 and 9 might have made it too easy, almost solved the puzzle, leaving only one integer left under ten would have suggested the right answer for the wrong reason.

    • The original sequence is a well-known puzzle in the maths community. (See the the second answer here for the full explanation of it’s solution.)

      As an amateur puzzle creator, my goal is often to take common math ideas and play around with them until I come up with a new riddle that is enjoyable and leads to good problem solving discussions.

      What’s funny is that I KNOW certain people will see my riddles and (happily) feel compelled to try to solve them. And I know that because I’m the same way.

      Some of my puzzles are just as a math joke, like this one: