# What constitutes a "puzzle," exactly?

Sorry for posting this, as I am sure this has been asked before, but what exactly makes a "puzzle?" For example, what if posted a puzzle like this:

I am the lowest number for which the Collatz conjecture does not hold. Who am I?

Obviously this is a mathematics problem, so it is not a puzzle. But there is a well-known puzzle called the "Locker problem" which is as follows:

I have 1000 lockers, numbered 1-1000. First, I open every locker. Then I close every other locker (starting with 2). Then I open/close every 3rd locker (depending on whether it is already open). Then I open/close every 4th locker, then every 5th, and so on. Once I've done that 1000 times, which lockers are open?

If a number has n factors, it will be opened/closed n times. Most numbers have an even number of factors, so those lockers will be opened/closed an even number of times, meaning they will be closed at the end. However, square numbers have an odd number of factors, meaning they will be opened/closed an odd number of times, so they will be open at the end. The only lockers that will be open at the end are the lockers whose numbers are square.

Is this problem a "puzzle?" It contains more and higher-level mathematics than the first one, yet it seems like it is more of a puzzle. So is there a way to define boundaries for what qualifies as a puzzle?

• – Gareth McCaughan Mod
Oct 31 '16 at 17:11
• If you are asking "how do I tell if a question is on-topic for puzzling.SE", this is probably too broad to get a reasonable answer. If you are interested in the specific examples you give, there are probably reasonable answers (IMHO they are "off-topic" and "on-topic", respectively), but I suggest you narrow the question down. Nov 1 '16 at 15:38