Has an Olympic Basketball (Men) game ever ended 81-69?
Exactly once. On July 23, 1976, Canada beat Australia 81-69, and no Olympic Basketball (Men) game before or since has ended that way. When it happened it was a scorigami, the first 81-69 in league history.
That makes 81-69 the 126th most common final score out of 698 that have ever occurred in Olympic Basketball (Men). One point away, 82-69 has happened never and 81-70 has happened 1 times.