In the first novel and radio series, a group of hyper-intelligent pan-dimensional beings demand to learn the Answer to the Ultimate Question of Life, The Universe, and Everything from the supercomputer, Deep Thought, specially built for this purpose. It takes Deep Thought 7½ million years to compute and check the answer, which turns out to be 42.
The Ultimate Question itself is unknown.
Lacking a real question, the mice decide not to go through the whole thing again and settle for the out-of-thin-air suggestion "How many roads must a man walk down?"
from Bob Dylan's protest song "Blowin' in the Wind".