The invasion is in a closed environment (no reinforcements)

And therein lies the fatal flaw in this assignment. Castles, broadly speaking, are not intended to operate in isolation, indeed they are quite often purposefully designed to delay an invading army specifically for the purposes of allowing reinforcements to arrive and lift the siege. English castles function perfectly in the wars of 1173 and 1174 in Scotland: in 1173, a Scottish invasion is delayed sufficiently before the walls of Alnwick and Wark that William Marshall has time to muster an English army and march north. When the Scots return in 1174, repeated attempts to storm or force surrenders succeed only at Brough Castle, forcing William the Lion to invest Alnwick Castle for a long siege. This delay allows the garrisons of Carlisle, Newcastle, Prudhoe and others to combine and defeat the Scottish army outside the castle.

A long siege can be incredibly costly and dangerous for an attacker. As William found out at Alnwick, the need to spread out your forces can leave them vulnerable to counter-attack, while siege camps themselves are breeding grounds for disease. This putitative scenario can also vary wildly on the topography and geography to hand, as well as prior conditions. We should assume, for example, that the castle has its own water supply, but what exists in the surrounding district? Before the Siege of Jerusalem, for example, the Seljuk defenders took great care to poison any available wells in order to deny any ready sources of water to the First Crusade. They also attempted to destroy or remove any stockpiles of timber or sources thereof; had Bohemond of Taranto not discovered what is likely to have been the hidden stash of a local timber merchant trying to protect his wares, the Crusade forces are unlikely to have been able to storm the city as quickly as they did, and the lack of water sources would have become a significant issue. In your scenario, your teacher has 3,000 horses to provide water for, before he even considers his 6000+ men. And that's before we bring food into the equation. To return to the First Crusade, the Siege of Antioch put the entire Crusade in jeopardy: the city had far more supplies than the Crusade, and faced with starvation there are reports that many Crusaders resorted to drinking horses' blood and even cannibalism to survive. Many more simply died. In the end, the city only fell because a turncoat was persuaded to leave a gate open and allow the invaders to sneak inside.

We also have to consider the composition of your attacker's forces and the resources available to him. 3,000 mounted knights, for example, are not particularly effective if they cannot get over the walls. This was the conundrum faced by William the Lion in 1174: a slow-moving siege train made his army vulnerable to English counter-attack, but without one, his army simply lacked the equipment to be able to effectively storm a large fortified site. Attempts to build such equipment, such as at Alnwick in 1173, met with disaster.

To take this situation to its logical absurd, therefore, we have to assume that if the castle in your assignment is forced to operate without reinforcement, then the 'closed environment' similarly preempts your attacker from receiving any external logistical support. As long as you have a well, a well-stocked granary and suitably high walls, simply inform your attacker that you've poisoned the local wells and stripped the surrounding region of both wood and supplies, and wait for his forces to die. I hope he brought at least 30 tonnes of hay a day or those horses are going to get hungry.

You may want to go for an early trace italienne style design. It's late medieval and a response to the introduction to gunpowder. It used triangle shaped bastions to avoid dead zones, rather than the turrets you would usually think of with a quintessential medieval castle.

It was further developed in the 16th and 17th century into the diamond shaped bastions you may still encounter in the Netherlands and France (amongst other places) but a full flung bastion would be outside of your medieval scope. Good luck!

Matriculations(may have spelt it wrong sorry) would also be a nice feature. It would allow soldiers atop the walls to attack down with out exposing them to enemy arrows like would happen if you just shoot over a ledge