# A Tough Logic Puzzle

Why not?

Iâm not sure how simple process of elimination can be considered a logic puzzle. Guess it depends on your definition.

I think most things most people call logic puzzles involve using logic to eliminate options as part of the process of solving the puzzle.

I agree that process of elimination is often a key part of logic or logic puzzles. I just donât see how by itself that would constitute a logic puzzle.

Here is what I would mean by a logic puzzle, Iâve posted this before but it was a long time ago and I canât remember where or when. The surprise quiz problem:

On Friday near the end of class the Philosophy professor tells the class there will be a surprize quiz sometime next week, so they should study this weekend to make sure they are ready. One student raises his hand and says âwell we know it canât be on Friday, since if we havenât had it by Thursday at the end of class it would mean itâs going to be on Friday, in which case it wonât be a surprise.â The professor agrees with that and says ok sure it canât be on Friday or else it wouldnât be a surprise, youâre right. But then the same student says âbut for that same reason it canât be on Thursday either, since if itâs Wednesday at the end of class and we havenât had the surprise quiz yet, and we know it canât be on Friday, then we know it must be tomrrow on Thursday. So it wouldnât be a surprise, we could just study Wednesday night.â The professor reluctantly agrees. Then the student repeats this same argument to eliminate Wednesday, Tuesday and Monday as possible dates for a surprise quiz. Confident that there will be no surprise quiz next week after having logically eliminated all possible days in the week, the student goes home and doesnât bother to study. Then on Wednesday next week, the professor begins the class by saying âSurprise! Quiz time.â

So where is the fault in the studentâs logic?

Wikipedia seems more liberal in itâs use of the term

It even lists sudoku as a logic puzzle, which is also generally solved by a process of logical elimination.

Good to see my dislike of and refusal to use wikipedia validated once again. Thanks.

There are logical inferences involved. Rules 4 and 12 are straightforward âcell X is Yâ, but itâs a logical inference from rule 11 and 12 that the oil painter isnât Canadian.. There are more complicated inferences down the line, patterns like âattribute A is either X or Z, but attribute B is either R or S, and if A is X, B canât be either R or S, so A must be Z.â

I agree yours is a logic puzzle, and that itâs a puzzle of a different kind. Iâd call FJâs puzzle one of âapplied logicâ, itâs a logic puzzle in the same way that âsolve for xâ is a math problem. I donât know what to call yours, maybe one of âlogical analysisâ? Youâre looking at someone elseâs applied logic and figuring out where it went wrong.

Good point about Sudoku though, I like those things. I can see how one might refer to them as logic puzzles. Process of elimination and all that. Ok, Iâll concede that it is the case that for any puzzle being solely processes of elimination if those processes of elimination are sufficiently many in number and sufficiently complex then we can reasonably refer to that puzzle as a logic puzzle.

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Iâd think in order to maintain some relevant differentiation and meaning to the definition here, we need to factor in the difficulty of the processes of elimination. Otherwise we would be forced to call âBen goes to the store to buy a banana or an apple. He doesnât buy an apple. What does he buy?â as a logic puzzle.

I guess technically it is, just a very very simple logic puzzle. Maybe one you would give to a small child who actually needs to think about it for a second.

Ok, you win. I concede that your original post here is a logic puzzle. Well played sir.

I think this puzzle is a little more challenging than youâre giving credit for. You can really only simply deduce about 6 spaces on the grid before you have to start applying some trial and error, or making a guess and hoping your guess stays consistent with the clues.

True, more difficult sudoku involve making educated or random guesses and testing them out to see if they work or not. That is a process of elimination of eliminating guesses until one of them works. Then you use simple process of elimination on the 1-9 in that row or column you can directly deduce. But Iâm not sure that âmaking guessesâ itself can be considered logical or a part of logic. Hypothesis testing is very important in many cases but would seem to be something other than logic, for example empiricism or brute force trial and error. Kinda the opposite of logic.

Oh it absolutely can. Itâs not uncommon at all to see a proof where theyâre not sure whatâs true, so they assume one thing is true, prove that that leads to a contradiction, and thus determine that that assumption cannot be true. Thatâs the process here too. Itâs parallel to how they prove that square root of 2 is an irrational number.

Itâs a proof by contradiction, and itâs a very important technique in logic and rhetoric.

Proof by contradiction yes. But trial and error brute force, thatâs something different.

If I donât know which of 5 doors has the prize behind it, but there are clues and various meanings about the doors I could work on logically deciphering to try and figure it out, but instead I just start opening random doors until I find the prizeâŚ thatâs more like abandoning logic, not using it.

Itâs logic in the sense that âifâ and âthenâ is used as in formal logic. It is logic to deduce that IF the guy in door 1 likes classical music, AND the guy that has grey hair is next to the guy that likes classIcal music, THEN the guy in door 2 has grey hair. That is a logical deduction that door 2 has grey hair, which is not stated in the clues.

I donât think theyâre mutually exclusive - try something, see if it produces a contradiction, if it does youâve proven that the thing you tried canât be true. Thatâs simultaneously trial by error and proof by contradiction, no?

By that we could say that a dog is using logic when it is digging up the ground looking for a bone it buried before but canât quite remember where the bone is. âIs it hereâŚ nope, is it over hereâŚ nope, is it over thereâŚ oh yeah here it isâ.

Is that really applying logic? I guess you could say the logic applied is something like, âwithin a given spatial grid, it is likely there is a bone buried somewhere in here. I will randomly choose areas to dig up until I find the bone.â That sort of process is unconsciously at work in the dog, just like if you have a dog in the car with you and you turn around a corner the dog will unconsciously shift its body in the opposite direction of the force caused by the turn, to maintain a stable center of gravity and not tip over. The dog doesnât KNOW or UNDERSTAND that itâs doing that, it just does it by instinct and feeling.

For me thatâs the difference. Logic should or does require conscious understanding and knowledge, at least that is what I mean when I think about what is logic. To say that we do things logically and unconsciously would be instead to say that logical processes have been encoded within us at the biological levels and we act these out without realizing it. Yes those things themselves are logical, but it would be incorrect to say that we are doing logic or applying logic when we do them. Like with the dog, it would be correct to say âthe biology of the dog has been structured in such a way as to cause the dog, when it feels motion in one direction, to automatically try to shift its body in the opposite direction a commensurate amountâ and we can call that biological underlying process involved a logical one, but it would be incorrect to say âthe dog is using logic to shift its body to prevent falling overâ.

I will distinguish between logic in-built as structural or unconscious aspects of systems, versus logic used or applied consciously with intent and understanding. Both of these things are referred to by using the same word, âlogicâ. Maybe they are both the same thing and one is simply consciously realized while the other isnât.

Anyway, let me know when you think youâve solved the Surprise Quiz problem.

âIs itâ and ânopeâ are not part of formal logic, âifâ and âthenâ are.

The dog gets to actually try - whereas, in logic puzzles like sudoku or the above, youâre only hypothetically trying. Youâre testing out the option mentally, logically, not submitting your try as an actual answer.

If I said âyou only get one guess at the answerâ, then you can still go away from the thread and do the process of trial and error without actually submitting your tries.

Whereas if I tell the dog you only get one try, and he digs one hole, well if heâs wrong then game over. He canât leave the grounds and mentally try out different digs before submitting his final answer.

Seems like a pretty big difference to me.

Thatâs not really the point I was making though. Whether you or the dog are actually testing out the possibilities in reality physically, or doing them in the mental headspace of imagination, doesnât really change what weâre talking about as to whether or in what instances should we consider such testing/trial and error to be either âexamples of logic itself albeit as rote unconscious biological structuringâ or âusing/applying logic with conscious intent and understandingâ.

It seems like the hugest difference to me. You can logically, mentally do trial and error for this logic puzzle. The dog cannot logically, mentally do trial and error for his bone. Thereâs no logic for him to apply, the bone could be anywhere. But in the puzzle above, the answers canât be anywhere, because some possibilities are logically impossible.