Lost Glyph Origin
奇 ( jī | qí ) is a character that means strange but the glyph origin appears to have been lost. At least as far as I can tell after researching offline books, zhongwen.com, and zdict.net ( qí ). The character is composed of (dà) 大 and (kě) 可 but none of my references can explain why the meaning is "odd" (numerically) or "strange" (as in unusual).
This is just one of the characters that seem to have lost it's history. I know that I could just accept it's meaning and memorise it but I really appreciate the storied history behind each character as a method to discern meaning. Can someone share information on the etymology of the character 奇?
I am also interested in how I should deal with discrepancies between Chinese and Chinese-English dictionaries in general (see below for an example). Often, I note that the Chinese dictionary has more information (whose implications I am missing) than Chinese-English dictionaries (is there a better method than just using a source like www.zhongwen.com)?
While researching this character I noticed that the Chinese dictionaries have much richer information available than the Chinese-English sources.
奇 jī ①形单的；不成双的（跟“偶”相对）。 奇偶 | 奇数 ②名〈文〉数目的零头。 身长六尺有奇 | 奇零 另见 qí。 奇 qí ①形特殊；稀罕。 奇形怪状 | 奇观 | 奇特 ②形出人意料的；不同寻常的。 奇遇 | 奇计 ③动惊异。 不足为奇 | 惊奇 ④副特别；非常。 奇冷 | 奇痒难忍 ⑤名姓。 用法说明读 qí，基本义是特殊、稀罕；读 jī，与数目有关，指单数或不成双的。 另见 jī。
(Simplified Chinese Dictionary)
a lot of which is quite hard to decipher and contrasted with my Simplified Chinese English Dictionary below:
奇 jī A.形容词 odd → 奇偶, 奇数 B.名词 书面语remainder 六十有奇 sixty odd → qí 奇 qí A.形容词 ①（罕见）unusual 奇男子/女子 remarkable man/woman 奇松怪石 unique pine trees and strangely-shaped rocks → 奇耻大辱, 奇迹, 奇妙 ②（出人意料）unexpected → 奇兵, 奇袭, 奇遇, 出奇制胜 B.动词 surprise → 不足为奇, 惊奇 C.副词 extremely 奇丑 very ugly 奇痒 be terribly itchy → 奇缺 → jī
Zhongwen.com hints that this may just be a person exhaling in wonder (to imply strange??) but is that a stretch?
Chinese Etymology seems to have very little information on this character (Source)
Zdict.net has a user forum (here) in which this character is discussed but I am afraid that I may have missed the gist of the conversation. So any help would be appreciated. The following reference image was shared in a post by user if that is any help. I am unsure of the original source and whether or not this is a composite.