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While studying yesterday, I came across the following sentence: "バスの中で お客さんの数を 数えました" (the spaces are included in the exercise). The meaning is simple enough, but when I asked my teacher whether that "の数" is necessary for the sentence to be correct, she said yes. I still don't quite understand, however, what kind of things you could use as a direct object with "数える". What exactly can be "counted"? I've seen at least one example where the word "人数" was used. Can you use any noun that doesn't end in "数" as the direct object (that is, as the receiver of the 'を' particle) with the verb?

Edit: I was looking at examples of using this verb on the JLearn website; And I think I might understand better what is going on. Although I would appreciate very much if someone with better knowledge of the language could explain it.

On the website, there are a few examples that use the 'を' particle with the 数える verb. Most of these have as direct object either the noun '数', being further specified by a 'の' like in the example I made, or some other word that ends in that kanji, such as 人数. One used what a similar word, '量'. Most of the others, however, seem to use a different construction; counting the object inside some class. Two examples of these are:

"君は私を君の友人のうちに数えてよい" "You can number me among your friends"

"彼は世界で最も偉大な科学者の中の一人に数えられている" "He is numbered among the greatest scientists in the world"

All of these examples seem to further use an indirect object to tell us what the direct object is being counted as. As A. Ellett mentioned in the comments, this isn't really counting; but an expression that sounds similar in English.

My suspicion is that the issue with not using the word '数', or some other similar one with this verb is that doing so would imply this second construction. There is one example that doesn't fit this, however:

"彼は薄暗がりと戦いながら、彼等の名前を数えていった" "Fighting the fading light he continued to count their names"

I am not sure why this sentence in particular works; but it was the only example where I found a noun that is not a number being counted without a "に" particle to indicate what it is being counted as.

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    It's worth pressing teachers farther than just "correct", because they may mean "you need to answer that way on tests because it's the structure we are studying right now" or they may mean "any other way would sound bizarre to a native speaker", and you have no way of knowing without getting more info from them.
    – Leebo
    Aug 25 at 23:48
  • Apologies, I should have been more clear. My teacher made it clear that saying "バスの中で お客さんを 数えました。" would have been grammatically wrong. Since we ran out of time, though, she didn't explain what kind of noun or noun phrase would be acceptable.
    – Alex
    Aug 26 at 1:19
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    I am unable to address the larger issue about counting the number of people. But, in the example you gave of 私を君の友人のうちに数える, this is not a literal count of anything. While in both English and Japanese (as this sentence indicates) you can say, "You count me amoungst your friends" ie "You consider me one of your friends". You are not counting in the sense of one, two, three, four...
    – A.Ellett
    Aug 26 at 2:25
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This is not a clear answer, but hopefully helps.

First, to me, バスの中でお客さんを数えた does not sound completely wrong. It is less natural, but I would say it is acceptable.

A possible explanation is that 数える can take a specific set of things as an object. So

  • 本を数えた I counted books

sounds rather strange, but

  • 本棚の本を数えた I counted the books on the shelf.

sounds OK.

I guess this is similar in English: I counted books should be strange while I counted the books might be acceptable. But Japanese does not have articles, restricting the books by a modifying phrase is the only possibility.

Back to your example, お客さんを数えた sounds strange, but having バスの中で, it is clear that you are talking about the passengers on the bus, so the sentence is acceptable.

Other examples

  • 電車でスマホを見ている人を数えた I counted the number of people watching smartphones on the train

  • 締め切りまでの日にちを数えた I counted the number of days before the deadline.

  • テーブルの上の空き瓶を数えた I counted the number of empty bottles on the table.

  • 残りのビールを数えた I counted the number of (cans or bottles of) beer left.

===

The only noun I came up with that can be used for 数える without any -数 noun or any modification is money: お金を数える 

Since this implies you are counting coins and notes you have, it may not be really an exception.

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    I counted books sounds perfectly fine in English, but it'd only sound natural in a limited number of circumstances: for example, what did you do while you worked at Amazon? As you properly noted, the issue in English is the use of the article; the verb to count though has no restrictions. Well, that is as long as the noun is a counting noun: you can't say I counted milk or I counted the milk. In the first, you'd have to say something like I counted bottles of milk. A case where English essentially requires a counter. I suspect that's the analogy for what's happening in Japanese.
    – A.Ellett
    Aug 26 at 11:55
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    I was wondering, though, with 彼等の名前を数える whether, if this sounds natural in Japanese, it's because 彼等の modifies 名前 (as your answer suggests) or whether it would also be natural to say 名前を数える (provided a context were given where that could make sense). Or would you really still just have to say 名前の数を数える. The reason I thought it might be able to stand alone was because 名前 was already close to its counter 名 and so the counter could be omitted??? (Not so much a question as that just seems questionable because surely 名前を五数えた sounds odd whereas 名前を五名数えた or 前を五つ数えた perhaps sounds better.
    – A.Ellett
    Aug 26 at 12:00
  • I see. Even if zero/definite article parallel does not work, the usage is still similar in that it requires context/restriction. お客さんを数えた alone can also sound ok with enough contexts (say, a waiter talking to a colleague in a restaurant).
    – sundowner
    Aug 26 at 12:43
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    彼らの名前を数える sounds fine, but when I think about it, the meaning is not very clear. He likely has a sheet of paper with a list of names. If he is really counting the number, then 名前の数を数えた is an alternative. Or he might be checking 彼らの名前 against the list, then 数えた is used in a figurative way.
    – sundowner
    Aug 26 at 12:57

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