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Natives of this gaming capital like to recall the days when they would ride horses in the desert that began just west of the glitzy Las Vegas Strip. Not anymore, pardner.

The U.S. Census Bureau has confirmed what harried local motorists have discovered in recent years: Nevada is the fastest-growing state.The desert and dude ranches that used to spread from the Strip west have been overtaken by housing developments and apartment complexes, springing up as fast as builders can move.

An estimated 5,000 people a month are moving here, drawn by the charisma of the city, plentiful jobs, low cost of living, nearly ideal weather, no state income tax and the dream of fortunes to be made.

Census Bureau figures released Wednesday show Nevada's population increased 50.7 percent the past decade, from 800,493 in 1980 to 1,206,152 in 1990.

Clark County, which includes Las Vegas, recorded most of that growth, jumping from 463,087 in 1980 to 735,892 in 1990, based on preliminary U. S. Census Bureau estimates. County officials disagree with the preliminary federal estimate, and say the county's current population is 769,152.

Washoe County, which includes Reno and is the state's second-largest population area, grew from 193,623 in 1980 to 260,000 in 1990.

Las Vegas natives, from gaming executives to celebrities who have played the city's showrooms, recall somewhat wistfully the days when Las Vegas was an overgrown western town.

The elegant ranch Las Vegan Wayne Newton bought "in the country" 30 years ago is today surrounded by housing and commercial developments.

Gaming whiz Steve Wynn likes to recall his first visit to Las Vegas in 1952, when he and his father would ride horseback across the desert that began at the edge of the budding Strip.

Today Wynn's $700 million, 3,100-room Mirage Hotel and Casino is the centerpiece of the Strip and has provided the impetus for the city's dynamic growth.

Construction of The Mirage sparked a multibillion-dollar building boom that has spread to all sectors of the economy.

Tourism and gaming continue to set records here, with 20 million visitors expected in 1990, according to Rossi Ralenkotter of the Las Vegas Convention and Visitors Authority. That's up from 11.9 million in 1980.