What's the difference between 何【なん】 and 幾【いく】 when referring to amounts?

Question

Is 幾 simply more literary/archaic than 何? Can 幾 only be applied to certain words whereas 何 is more versatile?

Answer 1

As far as the meaning, there is no difference. To say otherwise would be nitpicking.

The only (and important) difference is the way the words using 幾 and 何 as suffixes sound in our native-speaking ears. It is the classic "softer-sounding kun" vs. "sharper-sounding on" difference.

For instance, 幾重（いくえ）　sounds much softer than 何重（なんじゅう） though these words mean exactly the same thing --- "multiple folds" or "how many folds". One would opt to use the former in a poem or story, but if one used it in a daily conversation, one would look like a weirdo.

One could say 何 is more versatile because that is what we use much more often in real life.

Answer 2

I think they have just slightly different nuances. They are very similar; but, I think that 幾 has a more "specific" nuance (as in with relatively small numbers), whereas 何 has a more "broad" nuance (as in "to what extent" or "why").

For 何度, デジタル大辞泉 says:

１ どれほどの回数。また、多くの回数。何回。「―やってもできない」「―でも挑戦するつもりだ」

２ はっきりしない温度・角度などをさす。「気温は―ですか」

For 幾度, デジタル大辞泉 says:

１ どのくらいの回数。何度。いくたび。「―読んでもおもしろい」「―となく注意する」

２ （「いくどか」の形で）若干の回数。何回。いくたび。「―かお会いしたことがある」

３ （「いくども」の形で）度数の多いこと。たびたび。いくたび。「―も足を運んだ」

The entry for 幾 says:

１ 比較的小さな数について問う語。いくつ。「幾何(きか)」

２ 少しずつ。それとなく。「幾諫(きかん)」

３ （「機」と通用）細かいきざし。「幾微」

４ こいねがう。「庶幾」

And the entry for 日中 of 幾 is interesting, too:

疑問の代詞で,ほぼ1桁(けた)と予想される数を尋ねる

Maybe one could think of it as "how much" (何) vs. "how many" (幾)...