Continuing this week with the 2 kanji yo-ji theme, we're getting into military territory with 正々堂々.
正 means "true," or "regular." Shows up in 正しい （ただしい）and 正午 (しょうご）and makes things correct, or exact. Double it up, 正正, and you get 'accurate,' 'punctual,' or 'neat.'
堂 makes buildings. 本堂 is the main temple building, 食堂 is a cafeteria, etc. Doubled up, 堂々 is 'magnificent'... or just 'fair.'
1. Fair and square.
3. Energetic, vigorous, in an organized way.
This last translation comes from the origin of 正々堂々: Sun Tzu's Art of War. In fact, this yo-ji is a shortened version of this longer quote, translated from the original Chinese: 「正正の旗を邀（むか）うることなく、堂堂の陣を撃つことなし。」 My best translation is: Do not face off against the stately banner, do not attack the well-prepared formation. Not very a good rendition, but it gets the idea across. Imagine a flawless military regiment, in perfect formation, well drilled, and ready for action. It was one of Sun Tzu's most basic strategic concepts: Don't engage an enemy you can't beat; 正正堂堂した敵と戦わないように...
How it made the transition from the idea of high spirits, preparedness, and efficiency at war to today's more common usage, "fair and square," is less clear to me. Maybe it has to do with setting itself at odds with Sun Tzu's philosophy which was all about deception.
Note: I didn't know it at the time, but 風林火山 also comes from Sun Tzu.
Probably not a good idea to try to use the same yo-ji twice in the same sentence with two different meanings, but...
Sun Tzu advises not pitting yourself against someone who knows the rules better than you, but I don't want to go up against someone who doesn't play fair either.