Kōan

A kōan (公案^?) /ˈkoʊ.ɑːn/; Chinese: 公案; pinyin: gōng'àn; Korean: 공안 (kong'an); Vietnamese: công án) is a story, dialogue, question, or statement, which is used in Zen-practice to provoke the "great doubt", and test a student's progress in Zen practice.

Arousing this great inquiry or "Great Doubt" is an essential element of kōan practice.

Study of kōan literature is common to all schools of Zen, though with varying empahsises and curriculae.^[23]
Kōan practice is particularly important among Japanese practitioners of the Rinzai sect. 

Though few Soto practitioners concentrate on kōans during meditation, the Soto sect has a strong historical connection with kōans, since many kōan collections were compiled by Soto priests.
During the 13th century, Dōgen, founder of the Soto sect in Japan, quoted 580 kōans in his teachings.^[48]

Examples of traditional kōans:

Two hands clap and there is a sound. What is the sound of one hand? (隻手声あり、その声を聞け)

—Hakuin Ekaku

Thinking about Buddha is delusion, not awakening. One must destroy preconceptions of the Buddha.
One is only able to see a Buddha as he exists in separation from Buddha, the mind of the practitioner is thus still holding onto apparent duality. This is why Linji Yixuan said:

If you meet the Buddha, kill him. (逢佛殺佛，逢祖殺祖)

—Linji