Making them Multi-State Objects (MSO's) would give you what you want, but it depends on your deployment platform, as MSO's are not exactly universally supported.
Yes this is possible. For the grayed out state, you will need to create a second button for each.
I will use 10 blue button as an example:
Duplicate [10 blue], name it [10 blue gray].
Create the visual state for [10 blue gray] and make it "hidden until triggered".
For the [10 blue], you will add a second action: Hide/Show [10 blue gray]. This will go after the "go to destination" action.
Position both buttons over each other.
When you click 10 blue, you go to answer page, but when you return to home page, the grayed out button will now be active and stay active after further navigation.
*Make sure to remove "go to destination" on gray button if you don't want user to go back to answer page.
Thank you. This works beautifully.