Thanks for the question! So this game is definitely a bit different. We have three real estate companies, R, S, and T, and they’re going to trade buildings that they own with each other.
There are three types of buildings: class 1, class 2, class 3. We know the following distributions:
R owns G (class 1), Y (class 3), and Z (class 3) S owns F (class 1) and L (class 2). T owns K, M, and O, all of which are class 2.
Then we’re given rules about how the buildings can be traded.
1:1 trades of buildings of the same class One class 1 for two class 2s Two class 2s for two class 3s
And we should think about everything in terms of one base unit, which is the key to solving the game. So say a class 3 is worth one unit. Then a class 2 is worth two units (since you can get two class 3s with one class 2, so a class 2 is worth twice as much). Similarly, a class 1 is going to be worth 4 units (since you can get two class 2s with one class 1, so a class 1 is worth twice as much as a class 2).
Now, the way we’ve broken up the problem lets us conclude that each real estate company will start off with a certain number of units, and it will always end up with that number of units. Because you never gain or lose units, you just switch their kind. If you trade a class 1 for a class 1, you still have 4 units, just different buildings. Similarly, trading a class 1 for two class 2s will keep you at 4 units either way. And trading those two class 2s for four class 3s will still keep you at 4 units. No matter what happens, a company will keep the same number of units it starts with.
So now we can count up how many units each company starts with. R starts off with a class 1 and two class 3s, which is 4+1+1=6 total units.
S starts off with a class 1 and a class 2, which is 4+2=6 total units.
And T starts off with 3 class 2s, which is 2+2+2=6 total units.
So notice that each of the real estate companies starts off with 6 units, and they each have to always have 6 units throughout. Keeping this in mind will help us get through this game easily.
Hope this helps! Feel free to ask any other questions that you might have.
