An oracle told the people of Phrygia that fighting would end in their region when their new king arrived, riding on an oxcart.
Well Gordius, his wife and son (Midas!) arrived in the town by, surprise surprise, oxcart! The people trusted the Oracles word and made Gordius king. In gratitude, Gordius dedicated his cart to Zeus and tied it to a pole with an intricate knot. This was the Gordian knot.
The Oracle said that who ever could untie it would rule all of Asia. Many people came, but none of them could do it. Years later, in 333 BC, Alexander the Great came to Phrygia, now named Gordium, and tried to undo the knot. However, he couldn't find the ends of the knot to untie it. He became impatient and, in a fit of boldness, he took his sword and cut the knot in half.
For all of you people who slept through history class, Alexander the Great went on to conquer most of the known world, including Asia.
What in the world does that have to do with anything? Usually when someone uses the phrase "to cut the Gordian knot" they say it to mean act decisively and with boldness.
I've always taken the phrase to mean "think outside of the box".
It's hard to do that, especially with deadlines looming and grades at stake, but sometimes that's the only way to get something to work. Sometimes, it can actually save a lot of time and work out better for everyone in the end.
There's a story floating around the production of Pixar's The Incredibles. They needed to make the giant wave near the end of the movie. Brad Bird said he didn't care how it got done. If they needed to, they could make a giant wave in a swimming pool and comp it into the movie. Obviously they didn't do that, but it proved that he was open to doing something different to achieve a result.
When presented with a problem, try to think outside of the box. Cheat! Fake it! Everything we do is fake, so a fake fake isn't going to hurt anything if it looks good in the end.
Think of how much more we could learn if we were willing to look for alternative solutions.