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It was a tough year for Nintendo, including a rocky start for the Nintendo 3DS handheld gaming machine, but the big price cut made by the company in July appears to have helped boost demand for the glasses-free 3D gaming experience.

Redmond-based Nintendo of America says the 3DS has now sold more than 4 million units in the U.S. in its first nine months. The company said sales of SuperMario 3D Land and Mario Kart 7 for the 3DS have each surpassed 1 million units in the country, and the interest in those games has contributed to the stronger sales of the device.

The company says the 4 million milestone for the 3DS is more than the Nintendo Wii sold in its first nine months on the market. It might seem like an odd comparison, since the Wii is a home console, but the 3DS launch price of $250 was actually the same as the Wii’s launch price — which was one reason for the lackluster initial response to the 3DS.

Historical stats show the Wii selling 3.8 million units in the Americas overall in its first three quarters on the market, but that also reflected supply constraints. People who tried to buy a Wii at the time will remember they were tough to get.

For 2011 on the console front, Nintendo says it sold 4.5 million Wii units in the U.S. over the past year.

By comparison, Microsoft had sold about 5.1 million Xbox 360s in the U.S. not including December, traditionally the peak month for console sales. Microsoft hasn’t yet released its Xbox 360 unit sales for the full year.

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