See the linked question on Math SE:


The OP and others were confused about whether "the number of people who do not know an odd number of people" refers to

  1. People who know an even number of people, or

  2. People for whom the number of people they do not know is odd.

I'm aware that option 1 is the correct choice, and I answered the question without thinking twice. But someone whose first language wasn't English had no idea how to interpret it, and I attempted to explain why option 1 was correct. My attempt was poor. Can anyone here do better?

  • 5
    It is ambiguous -- both answers are equally "correct".
    – Hot Licks
    Commented Jul 28, 2016 at 0:20
  • 1
    @HotLicks I disagree. I read it as (do not) (know an odd number of people). (Do not know) (an odd number of people) sets off my "not English!" alarm. Commented Jul 28, 2016 at 0:23
  • Actually, my first interpretation would be #2, but I can see it would be argued either way. A lot has to do with the extent to which you tend to aggregate towards the left vs the right.
    – Hot Licks
    Commented Jul 28, 2016 at 0:28
  • @HotLicks well with the alternative interpretation the answer to the question is actually yes, but phrasing it that way seems bizarre. In that case you'd have a graph with an edge between two people if they do not know each other, and the number of vertices incident to an odd number of edges has to be even. But I can't imagine anyone asking the question and intending that answer, and I still can't convince myself that that could possibly be correct. Commented Jul 28, 2016 at 0:40
  • 1
    In mathematics one can assume that if A knows B, then B knows A. But this is English, and knowing a person is not a symmetric relation in English. That pretty much kills off the simple graph solution; you'd need directed edges at least. As for the unclarity, it's par for the course when you have a negative and two different quantities that have to be calculated at runtime in a short sentence with multiple phrasal repetitions. I.e, it isn't supposed to be clear -- it's confusingly written -- and it's not surprising that somebody couldn't understand it. Commented Jul 28, 2016 at 2:24

2 Answers 2


You knew it was true because of your background; you understand the question in the context it is given. Thus while there is nothing conclusively guiding you to one interpretation or the other in the grammar and syntax itself, you intuit the probable meaning based on the grammatical and syntactical formulations common to the context of the question. Your past experience informs your decision.


Let us say that I (Andy) am in a room with Bob, Claire, Danielle and Em, and I only know Bob.

I know Bob. Bob, as one person, is an odd number of people. Hence it is perfectly defensible, when talking about the people in the room, to say "I know an odd number of people".

I do not Claire, Danielle, or Em. Claire, Danielle and Em are an odd number of people. Hence it is perfectly defensible, when talking about the people in the room, to say "I do not know an odd number of people".

Hence, both are equally valid, logically and grammatically.


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