The pilot reported that while on a cross-country flight, in a single engine airplane, and as the airplane was about 30 miles from the destination, the engine began to surge and lose power. In an attempt to restore full engine power, he switched the fuel selector valve from the right fuel tank to the left tank, placed the fuel mixture to the full rich position, and turned on the auxiliary engine fuel boost pump. He said that the engine regained full power momentarily, but when the airplane was about 17 miles for the destination, the engine began surging again. He placed the fuel selector valve back to the right tank, but engine power was not restored. The pilot then selected a mountainous tundra-covered ridgeline as a forced landing site. During touchdown on the soft terrain, the nose wheel struck an object beneath the tundra, and the airplane nosed over, coming to rest inverted. The airplane sustained substantial damage to the wings and fuselage. The day after the accident, during a telephone interview with the National Transportation Safety Board (NTSB) investigator-in-charge (IIC), the pilot stated that he had failed to verify the amount of fuel onboard before departing. In the pilot's written statement to the NTSB, which was completed and submitted by the pilot's attorney, dated 11 days after the accident, he reported that 20 days before the accident he had the airplane fueled and verified that the fuel tanks were full. He stated that he flew two short flights, then the airplane sat for 12 days until the day of the accident flight. The accident flight occurred a day early and followed a different route than the pilot had anticipated to fly. The pilot stated that they flew extra miles and encountered significant headwinds and decreased ground speed before the engine began surging.