# Is it okay to assume a that question involves mastermind?

Some time ago there were some acquaintances that shared a puzzle with me. Essentially the same as the one here Crack the lock code with different graphics. After coming to the conclusion that there are two answers to the puzzle, as stated in the answer I eventually posted, some discussion ensued. The discussion basically boils down to truthiness of the statement "two numbers are placed wrong" if you compare 062 to 206.

I came to the puzzling stack exchange expecting to find some answers that would support my conclusion that the answer to the question "Are two numbers placed differently if you compare 062 to 206?" is yes. I did not find such an answer so I posted one myself.

To make the answer to the posed question be "no" requires making some assumptions, mainly that two numbers means exactly two numbers. The fact that some of my acquaintances made these assumptions without questioning and argued that they are right appeared to me as a representation of everything wrong with society /s. Of course, the next day I did not care about it much, but I stumbled upon my answer again and was reminded of it.

Assuming that the question posted was missing a changes the meaning of the question. Based on my sample size of two questions on puzzling and said acquaintances I still feel sad, that I was the only one answering those questions and not applying some rules that are stated nowhere in the question. I am petty!!! Tell me I am right!!! But seriously, am I the only one seeing it like this? The title is specific to mastermind, but I think the general idea of changing the question you are answering based some assumptions could be a more general issue to discuss.

I agree that the puzzle was ambiguous. (As a general rule, puzzles that take the form of brightly-coloured images are usually (1) bad and (2) plagiarized. Often they are also (3) deliberately ambiguous with the intention of misleading, though I don't think that's the case here.)

I don't think the "Mastermind" interpretation is unreasonable. (In particular, I don't think the accepted answer to the question is wrong.)

I don't think the puzzle turns on the subtler aspects of Mastermind rules as such, only on questions like "if I say that 'one number is a 3', does that mean the answer isn't 333?". The reason why it's reasonable (though, as I say, not necessary) to answer yes to that question is what fancypants philosophers call Grice's maxims of relevance. In the ordinary course of things, if you say "there is a cat in that box" everyone takes you to mean "there is a cat, and only one cat, in that box" because if you knew there were more you would have said "three cats" or whatever and if you didn't know how many you would have said something like "at least one cat".

I guess I should give a more explicit answer to the question in your title.

• Ideally, a puzzle should make its assumptions and meanings explicit and unambiguous (unless, of course, it's the sort of puzzle where part of the challenge is to figure out what it means, as for ones tagged here). If a puzzle doesn't do that, it's probably a good idea to ask the author for clarification.
• In this particular case, I'm pretty sure the author just lazily copy-pasted a puzzle from somewhere else, and probably had no idea what the intention of its maker was; and the maker probably wasn't working too hard to make a good puzzle either.
• Ideally, an answer to a puzzle whose wording is ambiguous should be clear and explicit about how it's handling that ambiguity.
• In this particular case, all the answers before yours assume (without saying so) "Mastermind"-type rules, or at least that "there are two Xs in Y" means exactly two rather than at least two; that's a flaw in those answers; your answer assumes instead (a bit more explicitly, though it could still stand to be clearer) that "there are two Xs in Y" means at least two rather than exactly two.

I'm not sure how the discusion part should function in this format, this "answer" is mostly in reply to Gareth McCaughan♦'s answer, but I will also try to elaborate why I think that making the assumption that mastermind rules apply should not be made.

First of all thank you for the answer. And I agree that for the example I gave the ambiguities could very easily be resolved by being more explicit about the rules and adding either at least or exactly to the rules.

Thank you also for the link to Grice's maxims of relevance, was a nice read. A quote from the wiki article:

Jeffries and McIntyre describe Grice's maxims as "encapsulating the assumptions that we prototypically hold when we engage in conversation"

As mentioned in the criticism part of the article what is "prototypically held" is somewhat cultural. I did not grow up playing mastermind so when I see that picture in the puzzle, mastermind is not what comes to my mind. To me the context of a logical deduction puzzle implies a different culture/context. More along the lines of sets in mathematics. In that context the answer to the question "if I say that 'one number is a 3', does that mean the answer isn't 333?" is no.

There are of course contexts in which if I say there is a cat in the box, then a single cat would be implied to be in it. Obviously the context I see in the puzzle is not the more popular one, as evidenced by the answers there, which is what was somewhat surprising to me and prompted me to write this question.

An example of me bumping into this in real life.

I somewhat recently added a category to my drivers licence. As part of that the DMV equivalent here tests your theoretical knowledge regarding the laws with a multiple choice exam.

The question: Who can be fined for driving without an insurance.

The choices:

• A) The driver
• B) The owner of the vehicle

The law they mean to test states that the driver has the responsibilty to make sure the vehicle he drives has insurance and would be fined if it is not insured.

The "correct" answer here was A. I answered A and B knowing what the law states. Afterward I disputed the fact that they marked my answer as wrong. It took quite a few emails to the DMV back and forth before they agreed to change the wording of the question.

Why B is in my opinion a correct answer here.

1. If you pose it as a question "Can the owner of the vehicle be fined for driving without an insurance?", then to me the answer is obviously yes.
2. If you draw a Venn diagram of drivers, owners and people who will be fined, there will be some overlap. That overlap is a subset of drivers and owners, therefore owners can be fined, given that they were also driving.

In a casual conversation I would probably not even notice the ambiguity in the DMV question and answer the "correct" option. But in the context where you have to concentrate and derive the answer based on laws and the question in front of you the context is different. And in my opinion the context in the logical deduction puzzle is closer to the DMV setting than to a casual conversation.