Edit in JSFiddle

// Challenge from: http://www.computedstyle.com/2010/12/hiring-front-end-engineers.html

(function(){
    var images = document.getElementById('slideshow').getElementsByTagName('img')
        ,current = 0, previous = 0;
    
    setInterval(function(){
        
        current += 1;
        
        if(current == images.length){
            current = 0;
            previous = images.length-1;
        } else {
            previous = current - 1;
        }
        
        images[current].style.display = "block";
        images[previous].style.display = "none";
        
    }, 3000);
})();

<div id="slideshow">
    <img src="http://1.bp.blogspot.com/_-dk1axrNmqU/TUIdKHlk51I/AAAAAAAANQU/2AdPWWik-wE/s400/honey.JPG" />
    <img style="display: none;" src="http://2.bp.blogspot.com/_-dk1axrNmqU/TUIaB-hGkhI/AAAAAAAANQM/IXqXWMAk8P8/s400/visit.JPG" />
    <img style="display: none;" src="http://4.bp.blogspot.com/_-dk1axrNmqU/TUIYrI9fczI/AAAAAAAANQE/UpimJkqu5p4/s400/airsystems.JPG" />
    <img style="display: none;" src="http://4.bp.blogspot.com/_-dk1axrNmqU/TUDMv6pi71I/AAAAAAAANP0/RqGr6AYk1fE/s400/artifacts.JPG" />
    <img style="display: none;" src="http://3.bp.blogspot.com/_-dk1axrNmqU/TUDL87HN_VI/AAAAAAAANPk/dzmkXEFv9jc/s400/crimefree.jpg" />
</div>