Koan (kung-an)

In Zen, a koan is a phrase from a sutra or teaching on Zen realization, an episode from the life of an ancient master ... each pointing to the nature of ultimate reality. Essential to a koan is a paradox, i.e., that which is "beyond thinking", which transcends the logical or conceptual. Thus, since it cannot be solved by reason, a koan is not a riddle. Solving a koan requires a leap to another level of comprehension. (Shambhala Dictionary of Buddhism and Zen, p.117.)