Consider how giving blueprints to Alice and Bob will affect the DIFFERENCE in their heights.

You want the difference to be 0, so you either need to add or subtract each G, and add or subtract some multiple of each R, and you want to get to 0.

Imagine the positive and negative Gs add up to k. Can you add or subtract copies of different Rs to get to 0? Suppose the rs to choose from are 4 and 6. What possible ks can you reach?

You can hit any k that's a multiple of 2. Specifically, any k that's a multiple of gcd(4, 6).

Notice that the sum of ground floors is bounded. There's an algorithm called 0/1 knapsack which tells you all the possible sums you could have if you take 0 or 1 copy of each element.