RENO, Nev.—Bernie Sanders could barely get a forkful of his 16-ounce ribeye from plate to mouth before another stranger in the crowded steakhouse barged up to his table asking for a selfie.

Mailmen in town for a conference, the harried waitresses and wide-eyed diners all wanted their moment with the bespectacled, disheveled Democratic presidential candidate and Vermont senator who has improbably emerged as a hot ticket on the 2016 campaign trail.

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