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I looked up `ありがたい` in my dictionaries within OSX (looking at [this
question](https://japanese.stackexchange.com/q/17584/78)), and one of the 国語
dictionaries (can't tell which) has the entry listed like this:

> **ありがた・い 【有り難い・難有い】**

You'll notice that the kanji in the second representation have swapped order.
Is/was this an accepted spelling for `ありがたい`, or is this likely just a typo in
this dictionary?
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kanji spelling i-adjectives
Alternate spelling for ありがたい, or typo?
Looking through BCCWJ, I find the following examples

> 其上的まで遣はすとは、何と **難有い** 御沙汰であらうがノ！
>
> 右に同じ猫伝をほめてくれて **難有い** ほめられると増長して続編続々編抔をかくきになる
>
> 人を救おうと云う **難有い** 志に感ぜず
>
> 先天地の御恩ほと **難有き** 物ハあらす

so it appears that 難有い can indeed be read as ありがたい.
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answer
Shogakukan does list the 難有 combination with a reading of ありがた in one place,
in the title of a kabuki play: 難有御江戸景清. Poking around online suggests that
this is read as ありがたやめぐみのかげきよ. The reversed kanji order would match Chinese
syntax better than Japanese, making me wonder if this is simply a _kanbun_
style of spelling.

EDIT:

Googling a bit more brought up [this OKWave
Q&A](http://okwave.jp/qa/q928057.html) wherein the "best answer" claims that
this is originally the spelling for かたじけなし, changing in meaning over time to
be ありがたい and then used with that reading. However, the etymology for かたじけなし
does not seem to have anything to do with 難い, at least according to
Shogakukan, and using 有 for なし seems far too much of a stretch.

[This goo thread](http://oshiete.goo.ne.jp/qa/928057.html) seems to confirm my
suspicion, that 難有い is simply the _kanbun + kun'yomi_ spelling of 有難い, as
suggested by their _kanbun_ example of a different word using 難い where the 難
kanji comes first in the spelling, but the かたい reading comes second in the
pronunciation.
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