# How can a logic puzzle be defined?

Myself and two others had a debate earlier over what separates a logic puzzle and a riddle.

Friend A was arguing that a logic puzzle was a puzzle that required any kind of logical and lateral thinking, although he didn't define what logical thinking is.

Friend B was arguing that a logic puzzle is one that can be solved with an explicit set of instructions, thus resulting in a computer programme being able to solve a large number of logic puzzles using a single programme.

How the debate started

One of them gave a puzzle for us to solve:

You are in a room with 3 switches. One of the switches powers a light bulb in another room. The only way to check which switch powers the light is by walking into the room to check. You can only walk into the room once, and can not walk back into the room with the switches. How can you find out which switch powers the lightbulb?

The answer is to switch one on, wait a while, switch it off and then switch a different one on. Walk into the room. If the light is warm, you know it was the switch that you turned on and off. If the light is on, you know it is the switch you turned on and did not turn back off. If the lightbulb is neither warm nor on then it is the other switch.

Friend B argued that this is a logic puzzle based on the fact that you had to use his idea of 'logical thinking' and lateral thinking.

Friend A argued that it is not a logic puzzle because of the fact that you have to think qualitatively about the fact that the light bulb will warm up, and it is in fact a riddle of some description. A ridiculously long code would need to be written in order for a computer to solve this puzzle, because the computer would have to have so much information stored in the code in order to think of the fact that a light bulb warms up - i.e. only humans can do that.

Who is correct? (Person B's argument convinced me, whereas person A's argument wasn't really an argument with any basis.)

• I don't think this question deserves a close-vote. Although some "opinion" plays into it, the question is exactly the opposite: Asking for some pro-found arguments for either side. Where, if not on PuzzlingSE should such a question go? I do think we should downvote "opinion"-based answers though – BmyGuest Feb 17 '16 at 18:43
• A logic puzzle about logic puzzles >.< – Daedric Feb 17 '16 at 18:45
• On the one hand, I agree with @BmyGuest, especially since the site descriptions include mention of creating and studying puzzles. On the other hand, in my experience, I feel like I see this question on the Meta(.puzzling) site more often than on the "main" puzzling site. – question_asker Feb 17 '16 at 19:19
• @question_asker That's because Puzzling has turned into a majority-puzzle-content site. But I think we should cherish questions like this, which are about puzzles. That was part of the original intend o this site. The tag "puzzle-identification" is a bit wrong though. "puzzle-classification" or "puzzle-definition" would be more correct (but doesn't exist yet.) – BmyGuest Feb 17 '16 at 19:24
• This question and answer on meta are also relevant. – f'' Feb 17 '16 at 19:35

Borrowing language from fuzzy set theory, what you have is a crisp, binary decision imposed on a set of more than 2 values, at least one of which is fuzzy. Let me explain.

Your friends implicitly assume that puzzles can be crisply partitioned into logic and non-logic puzzles. This is not the case. There are at least 3 types: puzzles fully answerable by logical manipulation of the given information, puzzles requiring (substantial) logical manipulation but which also contain some lateral thinking, and puzzles that are fully or predominantly lateral thinking with very little formal logic, if any.

Here are some examples:

1. pure logic: Einstein's puzzle, as GentlePurpleRain mentions;
2. some logic, some lateral thinking: your light bulb puzzle; and
3. pure lateral thinking, no formal logic: How did the Police Know?.

Note that the term logic puzzle has been adopted by a certain class of truth-table puzzles, so there is some justification to your Friend A's claim. On the other hand, semantically, it is just as justifiable to include type 2 in the term logic puzzles as it is to consider smart phones to be phones even though they are also cameras and music players, etc.

Type 2 is obviously fuzzy, but there is a degree of fuzziness in the other types as well. Type 1 requires language comprehension, especially wordy forms like Einstein's Puzzle. Type 3 often requires some logical thinking, even if it isn't mentioned in the answer.

Instead of trying to measure the amount of logic in the question, I suggest looking at how many answers can be considered correct. Naively, logic puzzles have at most one correct answer, while non-logic puzzles have more than one correct answer. For example, the Police puzzle has many answers posted which are all consistent with the given information. Some of the answers are even contradictory. This is a hallmark of type 3 puzzles. However, for type 2 puzzles, it might only seem to have one answer because others haven't yet been suggested. For example, instead of relying on heat-dissipation, one could rely on non-instantaneous fade-out of the bulb's filament, at least in principle.

To sum up, logic puzzles constrain the set of correct answers by the information explicitly presented, while non-logic puzzles (for want of a better term) allow the set of correct answers to be constrained (so to speak) by information sourced elsewhere. Under this definition, your light bulb puzzle is a non-logic puzzle.

I think the most-common definition of a logic puzzle is one that requires the solver to make deductions using formal logic, like the famous Einstein's puzzle.

With this type of puzzle, you use only formal logic to come to conclusions.

e.g.
Given: If A, then B
Given: If B, then C
Deduction: If A, then C

(I'm no expert in formal logic, so the example is pretty simplistic, but it should serve to illustrate my point.)

Any puzzle that requires any kind of knowledge not explicitly provided in the puzzle (aside from the rules of formal logic) would not generally be considered a logic puzzle.

• We could take this further by discussing entailment – Will Feb 17 '16 at 21:36
• A good answer with a great example as that of Einstein's puzzle. – ABcDexter Feb 17 '16 at 21:56

Persons A and B are trying to draw a semantic distinction over language that is intrinsically ambiguous. As a result, neither of them are wrong.

If you want to have an argument of whether a puzzle is one of logic or not, you first need to clearly define what counts as "logic," and subsequently, what counts as a "logic puzzle." Neither of these things happened, which is the source of your argument.

I agree with GentlePurpleRain in principle - a logic puzzle is one where the answer is logically deducible from the information provided in the question. However, I think this still leaves semantic ambiguity.

It could easily be considered not a logic problem. If we're restricting "logic" to mathematical or formulable steps, then it's certainly not - the crux of the problem is in realizing the light bulb will be hot.

It could, however, easily be considered a logic problem, as well. You can logically deduce that flipping one switch does not give you enough information, and so you need to find another way to obtain the results. That, even, is mathematically expressible.

Obviously, you still need to build a way to actually do that, but the problem has logically expressible steps.

Ultimately, this leaves the difference as nothing but semantic.

This question is biased because the very 'riddle' (or 'logic puzzle') is biased: one piece of information is missing, i.e. the enunciation ought to include something like '[a lamp] whose one or more additional parameters other than visible light can be assessed'.

Whereas a lamp admittedly emits visible light, being able to measure or sense its temperature is not ascertained in all cases (the lamp might be out of reach or, if fitted with LEDs, its temperature increase might not be sensed straightforwardly). Without the additional temperature parameter, no computer could ever solve the riddle, for it could not suspect the very existence of the variable. If the 'can-the-temperature-be-sensed' parameter is registered as a boolean value, calculation will succeed only if it is true; otherwise it will lead to undecidability.

Tricky 'riddles' of the sort are not uncommon. If 'logic' is meant as a computable set of statements, then this one is no logic, whatever you may call it. Now if one thinks that 'logic' allows a recourse to undeclared variables, he may call it that —while he could not expect a computer to ever exploit loopholes.