It turns out that there is no one way to count Inca artifacts.

The Peruvian government announced Sunday that an inventory it conducted of Machu Picchu objects currently housed at Yale found some 40,000 pieces — about 10 times the number Yale had previously announced. But Yale officials said the discrepancy is a matter of mere arithmetic and not a sign of a significant disagreement.

Richard Burger, the Yale Archaeology professor who was responsible for creating an initial inventory of the pieces months ago, said he is not surprised that the Peruvian count is so much higher than his estimate of roughly 4,000 objects.

“Counting is complicated,” Burger said by telephone from Peru, where he is on an archaeological dig. “Do you count lots or do you count every piece? There may be tens of thousands of objects if you count each finger bone in a skeleton.”

The report, released by Peru’s minister of health, Hernan Garrido-Lecca, was the result of a March trip to Yale by officials from the National Institute of Culture in Peru. Cecilia Bakula, the institute’s director, led the Peruvian visit, which was at the time hailed as a step toward a final resolution in the nearly century-long dispute over rightful ownership of the objects.

The artifacts were excavated by Yale explorer Hiram Bingham III between 1911 and 1915. And while Peru has long maintained its claim to the ancient pieces, the trip last month was the first opportunity for Peruvian officials to verify independently Yale’s accounts of the collection’s contents.

University General Counsel Dorothy Robinson said last month that the trip was consistent with a mutual desire for a Peruvian expert to see the artifacts before a final agreement on their ownership could be signed. Robinson could not be reached for comment late Sunday night.

One of the biggest challenges in creating an inventory, Burger has said in several interviews over the last year, is the question of which pieces to classify as museum-quality and which to classify as non-museum-quality. Under the terms of a September memorandum of understanding signed between Yale and Peru, this distinction would be tremendously important.

Museum-quality artifacts would be returned to Peru after an international traveling exhibition and would ultimately be housed at a special museum built by Peru with Yale’s input. But some non-museum-quality objects would remain at Yale’s Peabody Museum of Natural History for another 99 years.

This last stipulation has exacerbated political tension in Peru and, Peruvian and Yale officials have said, has partly hindered the two parties’ efforts to reach a final agreement.

Yale’s Office of Public Affairs released the University’s inventory of the objects on its Web site last month. University Spokeswoman Helaine Klasky did not respond to a request for comment late Sunday evening.