# How do I do the Hard mode version of the 2nd bonus puzzle unlocked after beating level 45 in Hexologic?

In Hexologic, there are bonus levels that you can unlock after completing each 15 levels. (although it doesn't matter if it's on Easy or Hard mode) I have been able to complete all of the bonus levels on both Easy and Hard mode except for 2 of them, which I am attempting to beat on Hard. This is the puzzle layout:

I-

Anyways, there are some things that I am going to be able to do:

1. The bottom left 4 must be a 2-2 pair. If the 4 was a 1-3 pair, the 9 would not be able to be satisfied, and if it was a 3-1 pair, the 3 could not be satisfied. Some other deductions leads me to this board state:

1. Let's now focus on the green cell. If that were to be a 3, then the 4 must be a 1-3 pair, which then according to Hexologic rules, is impossible to satisfy. So the green cell must be a 1 or a 2. However, if the green cell was a 2, then the 5 makes a 2-3 pair, and then in the row containing 17, we would have $$3+2+4+7=16$$ which then we would need $$x+y=1$$ which is not satisfiable with our conditions. So the green cell must be a 1, which means that the 9 must be a 3-1-5 pair. Then we can satisfy the 4s, which gives this grid state:

however I'm unsure if I can logically deduce the solution from here. So my question is: