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Recently I saw a puzzle on Facebook. A kind of a puzzle I usually don't comment, but this one was interesting, because it wasn't a mathematical puzzle, which you could think at first - it was an english puzzle.

1 rabbit saw 6 elephants while going to the river. Every elephant saw 2 monkeys going towards the river. Every monkey holds 1 parrot in their hands. How many animals are going towards the river?

I'm interested in the particular usage of "every" in the second sentence. Most solutions to this problem think of a group of six elephant and that each one saw the same group of two monkeys. Therefore they're adding 2 to the total for the monkeys. But I would argue, that the usage of "All elephants saw [...]" would be more appropriate in that situation and that "every" is used iterative in this case and therefore indicating, that there were in fact twelve monkeys going towards the river. Another thought would be, that you could use "every" in both ways, which would mean, that there's an information missing and the solution would be somewhere from two to twelve monkeys.

This leads me to my question: Is "every" iterative?

Iterative? I'm Software Engineer, so this was the most accurate description to me. But I'm open to comments on this.

  • Your interpretation of every seems correct, as it is used in that way in _every monkey) as well. However, it seems to be physics that confuses things. If there are only two monkeys, it is entirely possible that they are observed by each and every elephant, and that would not change the sentence in the slightest. It could be possible that all elephants were visible to the rabbit, and that 6 groups of two monkeys were visible to only one elephant, which would require handy use of trees, I guess. The sentence wouldn't change. It's a facebook puzzle. – oerkelens Apr 6 '18 at 6:41
  • It sounds like a variant of the old riddle "As I was going to St.Ives", except that in this case everyone does seem to be headed in the same direction! – Kate Bunting Apr 6 '18 at 7:58
  • 'Every elephant' simply means 'each one of the elephants'. The ambiguity has little to do with the word 'every', but a lot to do with the identity of '2 monkeys'. This is hardly a problem about the use of 'every'. As a riddle, it's also very poorly thought out. What about the 43 monkeys none of the elephants saw? The 176 zebra? Were the elephants coming away from the river? – Edwin Ashworth Apr 6 '18 at 8:56
  • No. You can have a group of 3 monkeys, with each elephant only spotting 2 of them. Depending on how the viewings were counted, you might even be able to get away with just one monkey, appearing twice to an audience of your 6 elephants, though in this case, the wording of your quote doesn't quite allow that flexibility. – Lawrence Apr 6 '18 at 8:57
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Every itself is never multiplicative except by a factor of one. In fact, the entire history of the word is an attempt to emphasize a meaning of ‘one single member in a set’. Contracted from Old English æfre ælc ‘ever each’, appearing in Chaucer as everich, the word is often still felt to need additional emphasis such as every last, every single, or

Each and every student had two unique topics to consider, based on his or her special interest, discipline, or sub-discipline.

Now based on the verb had, we could turn this sentence into a math problem if we knew how many students there were in the class, assuming that unique means unique to each student rather than unique to each field of study. Every, however, is not the multiplier, but signals the multiplicand: the number of students multiplied by two equals the total number of topics.

The same is true for this statement:

Every student had two private lessons, one with me and one with Apprentice Swan who was the co-teacher during the week.

The number of students multiplied by two equals the total number of private lessons given by the speaker and Swan.

Seeing, however, is not the same as having or holding. If an event occurs which is observed by any number of people, then the only mathematics involved might be determining the number in the group, but that does not multiply the event. Whether you designate the group as all members of a set or as every member of the set, you still end up with the same number of people seeing one event:

When his comrades raced to his side, everyone saw three more of the mysterious men emerge from the swamp, walking in perfect formation, shoulder to shoulder.

Sure enough, far away, everyone saw three twinkling lights rising up in the darkness, to remain visible for half a minute or so.

No matter how many people witnessed the men emerging from the swamp or the lights twinkling in the dark, there were still only three, not three for each person who saw them. Every person, not just some, saw the same thing.

Thus, if one rabbit sees six elephants, then there must be six. But if every elephant, i.e., each of six, sees this rabbit are there suddenly six rabbits? So if the elephants see two monkeys, there are still only two. If every monkey holds a parrot, however, there are two parrots.

The charm of this puzzle lies in thwarting expectations for the genre “word problem,” where the reader assumes nouns and verbs are be abstracted into numbers and operations. The repetition of every — most speakers would say each monkey or even both monkeys rather than every — reinforces those expectations so strongly that you’ve posted a question here asking about the meaning of a word native speakers use constantly in a single, unambiguous sense.

The verb see cannot be parsed as an operation no matter how many are doing the seeing. Every can determine a multiplicand only when a verb like have or hold can be, but it still means what it’s always meant: one of a group.

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