Random color on different div's

You could use classes instead of ids and simplify your code to following.

// You could easily add more colors to this array.
var colors = ['red', 'blue', 'green', 'teal', 'rosybrown', 'tan', 'plum', 'saddlebrown'];
var boxes = document.querySelectorAll(".box");
var button = document.querySelector("button");

button.addEventListener("click", function () {
  for (i = 0; i < boxes.length; i++) {
    // Pick a random color from the array 'colors'.
    boxes[i].style.backgroundColor = colors[Math.floor(Math.random() * colors.length)];
    boxes[i].style.width = '100px';
    boxes[i].style.height = '100px';
    boxes[i].style.display = 'inline-block';
  }
});

button.style.cursor = "pointer";
<div class="box"></div>
<div class="box"></div>
<div class="box"></div>
<button>Enter</button>


Randomizing the colors on page refresh/load.

// You could easily add more colors to this array.
var colors = ['red', 'blue', 'green', 'teal', 'rosybrown', 'tan', 'plum', 'saddlebrown'];
var boxes = document.querySelectorAll(".box");

for (i = 0; i < boxes.length; i++) {
  // Pick a random color from the array 'colors'.
  boxes[i].style.backgroundColor = colors[Math.floor(Math.random() * colors.length)];
  boxes[i].style.width = '100px';
  boxes[i].style.height = '100px';
  boxes[i].style.display = 'inline-block';
}
<div class="box"></div>
<div class="box"></div>
<div class="box"></div>


How about this?

http://jsfiddle.net/stackmanoz/vymmb10s/

CSS-

div[class^="box"]{
    width:100px;
    height:100px;
    border:1px solid;
    display:inline-block;
    }

jQuery-

var colors = ['red', 'blue', 'green', 'gray', 'black', 'yellow'];
$(function(){
     $("#btn").click(function() {
     $('div[class^="box"]').each(function(){
        var randomColor = Math.floor(Math.random() * colors.length)
        $(this).css('background-color', colors[randomColor])
                                  });
});
});