"め" in "五匹め" implies some sort of "ordering"? Where it makes sense, the default is "time"?


`め` after a counter implies _some sort of ordering_ , right?

Say that you are shopping for a cat.

**scenario #1**  
You look into a room with 5 cats in it. Does saying `五匹めが好きです。` mean anything?  
In that context, saying `I like the fifth one.` sounds ridiculous.

**scenario #2**  
You look into a room with 5 cats in it. Then you have a dialogue:

> A-さん: 黒くって小さいのが好きですか。  
>  B-さん: そうですね。私の好みよく知っているよね。五匹めが好きです。

Could that mean that "B" likes the smallest black cat? The _ordering_ is
implied to be size?  
`I like the fifth one.` does not make sense.  
`I like the fifth **smallest** one.` makes sense.  
`五匹めが好きです。` only makes sense when you use context to imply in _size_ as the
ordering criteria.

**scenario #3**  
You are, one by one, shown 5 cats. Then you say `五匹めが好きです`。 And that means
that you like the 5th cat that was shown to you? Showing the cats sequentially
tees-up time as the criteria. There is no need to establish context.

**scenario #4**  
You are, one by one, shown 5 cats. Then you have a dialogue:

> A-さん: 黒くって小さいのが好きですか。  
>  B-さん: そうですね。私の好みよく知っているよね。五匹めが好きです。

Now, we have 2 possible ordering criteria. Since size is explicitly
established as the immediate context, implied "size ordering" supercedes the
default "time ordering"?




Among these scenarios, 5匹目が好きです makes sense only in Scenario 3. 5匹目が好きです never
means "the fifth _smallest_ cat" in any of these situations.

"The fifth smallest cat" is translated as 5番目に小さな猫 in Japanese (general rule
is found [here](https://japanese.stackexchange.com/q/13009/5010)). If you say
5番目に小さな猫が好きです, it's at least a valid and understandable Japanese sentence. Of
course, a normal person will never say such a thing when there are exactly
five cats in the room. They simply say 1番大きな猫 ("the largest cat")!




Among these scenarios, 5匹目が好きです makes sense only in Scenario 3. 5匹目が好きです never
means "the fifth _smallest_ cat" in any of these situations.

"The fifth smallest cat" is translated as 5番目に小さな猫 in Japanese (general rule
is found [here](https://japanese.stackexchange.com/q/13009/5010)). If you say
5番目に小さな猫が好きです, it's at least a valid and understandable Japanese sentence. Of
course, a normal person will never say such a thing when there are exactly
five cats in the room. They simply say 1番大きな猫 ("the largest cat")!

