The Green Box website has rules for 25 games published at the moment, across 3 different main categories. One of these is "Inspired", which contains adaptations of popular games from the past few decades. Some (like "Hey, that's my stuff") play more or less exactly like the originals, while others (like "Sutlers of Kansas") are more distant adaptions attempting to capture the feeling.
The rules are available in the inspired category:
Or as a pdf in the download section.
Here is a list of the games that have inspired those that are currently published:
Hey, That's My Fish!
I have also received a number of suggestions for games that can be adapted using the components of the Green Box:
If anyone wants to take a crack at writing up adapted rules for one of these games, I'll be more than happy to publish it with full credits on the website. Otherwise, I will get through the list myself in time.
Also, if you have other suggestions for games that you think should be playable with the Green Box, I'll be very happy to hear about them in this thread!
I show an adaption of ticket to ride for two players, using a special PiecePack, a regular deck of cards, and a set of dominoes.
I needed the extra cards, the extra beads, and the dominoes (to establish the destinations). But the green box has cards and cubes, so maybe it can be adapted better.
Ticket to Ride is a bit of a challenge to adapt, but I read your brief summary in the image comments, and I think you can do pretty much the same with the Green Box. And without the need for extra components.
The cards can be collected in sets either by colour or by symbol (suit). I would probably go for colour, so that you need a certain number of the same colour to connect two cities, but your set also needs to include at least one symbol matching the starting city and one matching the destination.
The tiles in the Green Box have only one characteristic, the symbol, but there are 6 different. You could build a map with half the tiles face up and half face down to work as blank space between cities that you need to cross. You could build either a perfectly checkered square map, or more of an odd shape with a random mix of face up and down tiles for extra variation. The latter would mean some connections are longer than others, needing more cards and scoring more points. Maybe even hexagonal, something like the boards I have suggested for War: https://greenboxofgames.com/2016/09/28/war/ Only more compact.
For missions, you could take out some of the cards (like all the 9 blacks and a few of the whites, leave the rest of the whites in as wild colours) and build sets of cities you need to connect. Or, as a simple add-on in terms of components, you could create some simple "mission cards" on pieces of paper, just jotting down a combination of symbols on each "card".
There are only 20 cubes of each colour in the box, but for two players you can use two colours each.