Has an Olympic Basketball (Men) game ever ended 81-61?
Exactly once. On August 2, 2012, Australia beat China 81-61, and no Olympic Basketball (Men) game before or since has ended that way. When it happened it was a scorigami, the first 81-61 in league history.
That makes 81-61 the 126th most common final score out of 698 that have ever occurred in Olympic Basketball (Men). One point away, 82-61 has happened never and 81-62 has happened 1 times.