YukicoderRainbowColor.user.js

// ==UserScript==
// @name        YukicoderRainbowColor
// @namespace   YukicoderRainbowColor
// @description 解いた問題の色を虹色にするスクリプト
// @include     http://yukicoder.me/*
// @include     https://yukicoder.me/*
// @version     2
// @grant       none
// ==/UserScript==

(
function(){
var key_frame = "" +
"      0% {background: #e0faea;}" +
"     16% {background: #e5f5ef;}" +
"     33% {background: #eaf0ea;}" +
"     50% {background: #eff5e5;}" +
"     66% {background: #eafae0;}" +
"     83% {background: #e5ffe5;}" +
"    100% {background: #e0faea;}";

var key_frame_hover = "" +
"      0% {background: #c0caea;}" +
"     16% {background: #c5c5ff;}" +
"     33% {background: #eac0ea;}" +
"     50% {background: #ffc5c5;}" +
"     66% {background: #eaeac0;}" +
"     83% {background: #c5ffc5;}" +
"    100% {background: #c0caea;}";

var new_css = "" +
"  tr.solved:nth-child(3n+0) {" +
"    animation         : rainbow 1s -0s linear infinite !important;" +
"    -moz-animation    : rainbow 1s -0s linear infinite !important;" +
"    -webkit-animation : rainbow 1s -0s linear infinite !important;" +
"  }"+
"  tr.solved:nth-child(3n+1) {" +
"    animation         : rainbow 1s -0.33s linear infinite !important;" +
"    -moz-animation    : rainbow 1s -0.33s linear infinite !important;" +
"    -webkit-animation : rainbow 1s -0.33s linear infinite !important;" +
"  }" +
"  tr.solved:nth-child(3n+2) {" +
"    animation         : rainbow 1s -0.67s linear infinite !important;" +
"    -moz-animation    : rainbow 1s -0.67s linear infinite !important;" +
"    -webkit-animation : rainbow 1s -0.67s linear infinite !important;" +
"  }" +
"  @keyframes rainbow {"         + key_frame + "}" +
"  @-moz-keyframes rainbow {"    + key_frame + "}" +
"  @-webkit-keyframes rainbow {" + key_frame + "}" +
"  tr.solved:hover {" +
"    animation         : rainbow-hover 0.5s 0s linear infinite !important;" +
"    -moz-animation    : rainbow-hover 0.5s 0s linear infinite !important;" +
"    -webkit-animation : rainbow-hover 0.5s 0s linear infinite !important;" +
"  }" +
"  @keyframes rainbow-hover {"         + key_frame_hover + "}" +
"  @-moz-keyframes rainbow-hover {"    + key_frame_hover + "}" +
"  @-webkit-keyframes rainbow-hover {" + key_frame_hover + "}" +
"";

var node = document.createElement('style');
node.type = "text/css";
var txt  = document.createTextNode(new_css);
node.appendChild(txt);
document.head.appendChild(node);

})();

Greasemonkey / Tampermonkey 等をブラウザにインストールした状態で、右上にある [Raw] をクリックしてインストールしてください。
ライセンスは NYSL でお願いします。 http://www.kmonos.net/nysl/

パワーアップしました。 gradient も使おうかと思いましたが、面倒なのでやめました。