I often wonder about the difference between a Problem and a Puzzle.

e.g. Why is ‘how long does it take to fill the bath?’ a problem, but ‘how far does the fly travel?’ a puzzle? (That last part will make more sense shortly, when we get to the fly puzzle.)

I suppose the simple answer is: ‘puzzles are fun’, but that won’t fill a page. So, instead, I’ll make some observations on things that many puzzles seem to have in common which help to differentiate them from problems.

The first is: a puzzle is usually easier to solve than you initially think. This is the case with both the ‘Two Trains One Fly’ puzzle, and with this geometry puzzle from Richard Wiseman (at the bottom of the page). The first of these is especially interesting because there’s a famous story about John von Neumann solving the fly puzzle ‘the hard way’.

Another thing, which often goes hand-in-hand with the first is: misdirection. For example, phrasing the puzzle in such a way that it seems to be harder than it is, or giving a hint which sends you in the wrong direction. The ‘Seven Dots Problem’ is a good example of the latter.

A third thing is: beauty. This is harder to define, but it might be that the way you find the answer is remarkably simple; or there may be something interesting about the answer itself – a nice round number, or even just the number you first thought of. A good example is the ‘Weigh The Pearls Problem’ - I think that this problem would be harder if there were 8 pearls rather than 9 (because the 8 will misdirect the player), but the solution is more beautiful with 9.

The title of this post originally included the word ‘Game’ – because I had planned to also discuss how hard problems can make good games – but I’ll leave that for another post.