Koan in Chinese / Japanese...

In the Buddhist context, 公案 is a Zen question for meditation.

From the Buddhist dictionary, this is:
Problems set by Zen masters, upon which thought is concentrated as a means to attain inner unity and illumination.

The secular meaning of this word can mean a judge's desk, a complex legal case, a contentious issue, a dossier, a case record, public laws, regulations, or case law.

大道無門 is a Buddhist proverb that means “The Great Way has no entrance,” “The Great Way is gateless,” or “The Great Path lacks a gate.”

This can be translated in many other ways.

This concept was authored within a long sacred text by 無門慧開 (known as Wúmén Huìkāi in Chinese or Mumon Ekai in Japanese). He was a Chinese Chan Master (in Japanese, a Zen Master) who lived between 1183 and 1260 AD. His most famous work was a 48-koan collection titled “The Gateless Barrier” or “The Gateless Gate” (無門關 Wú Mén Guān in Chinese, or 無門関 Mu Mon Kan in Japanese). This calligraphy title is a notable line from this collection.

I like this reference to the source of this proverb: The Gateless Gate 無門關

This controversial Buddhist koan means “On encountering Buddha, you should kill him.”

This is the short concise Japanese version of an original statement by ninth-century Chinese Buddhist monk Linji Yixuan, “If You Meet The Buddha On The Road, Kill Him.”

This takes some explaining... The concept here is that if you think you have seen, experienced, or achieved true enlightenment, the chances that you really have are so slim that you should kill or dismiss that idea.

Another suggestion is that one's path to becoming a Buddha is one's own, and one should not get caught up in religious fervor, and avoid “showing off” that they are a Buddhist.

Helpful references for this concept:
Lion's Roar addresses "If You Meet The Buddha On The Road, Kill Him"
Kill the Buddha

Note: Because this selection contains some special Japanese Hiragana characters, it should be written by a Japanese calligrapher.