Yeah, way to go AJ. We were fighting your team beside us throughout the contest, but I guess they got the better of us in the end. Looking forward for another chance to beat Waterloo and Massey at York.

I enjoyed how the contest was so balanced at our regional this year. It seemed like a bunch of teams had a good chance to move on but in the end it was the usual suspects once again.

Hoping the next round doesn't have another hard code style question like #2 was as those problems generally come down to bugs in the code and how fast you can type rather than finding the correct algorithm.

I believe I have a pretty simple solution for #4.
For a 3x3 grid, we determine the number of moves for every target grid. To determine the number of moves, there are a couple key observations:
1) This one's obvious. It's always optimal to begin by filling empty spots with the correct number, as long as the correct number isn't somewhere else in the board.
2) Once all the numbers are in place, determining the number of swaps can be done with a simple greedy algorithm: Go through every square, and if the current square contains the wrong number, find the square with the correct number and swap them.

So the algorithm is as follows:
Fill in all the empty spots with the correct numbers, where possible.
Try every permutation of the numbers that haven't been placed on the grid (this is also really easy with languages that have a permutations function), and place them on the grid in that order.
For each of these permutations, determine the number of swaps and take the minimum.

This algorithm runs very fast because in the worst case there are 4 unplaced numbers after filling in the empty spots, and 4! permutations is no big deal (and none of their test cases had more than 3 remaining numbers).
Unfortunately, my team only finished 5th in the centre region because we made the most trivial mistake imaginable on #3 - we forgot to convert the angle to radians (for the Python math module). So frustrating!