Codeforces 478D Red Green Towers - State Definition

Why can't we use $dp[i]$ = "ways to build first $i$ levels"? Because knowing you've built 5 levels tells you nothing about how many red blocks you've used. Two different colorings might use completely different amounts of red.

You need to track both: $dp[i][j]$ = "number of ways to build the first $i$ levels using exactly $j$ red blocks." Now a state like $dp[5][10]$ means: "I've built levels 1 through 5, and I've used exactly 10 red blocks so far (out of the $r$ red blocks available)."