In the original Super Mario Bros., in the X-1 stages (2-1, 3-1, etc.) there are hidden 1UP mushrooms.
Sometimes they're there, and sometimes not. But what's the key? Why are they so fickle? In How to Win at Nintendo games Jeff Rovin thinks he's figured it out. Page 191 says:
[In level 5-1] [w]hen you reach the second floating Block (behind the wall) you'll find a One-Up Mushroom between them ... but only if you haven't been hurt prior to reaching the area.
Now, this is partly right, the mushroom is right there... sometimes. Getting hurt has nothing to do with its appearance, though. There are two ways to make them appear.
In the prior X-3 world (in the case for 5-1, it'd be 4-3) you have to have collected all of the coins.
You have to have warped directly to that world (i.e. warp to world 5, the 1UP will be there).
Works every time.
For their locations, I humbly suggest that you take a look at a prior pro tip.
And that wraps up this week's myths. We'll return to regular ol' pro tips next week.