In the video game, Shadow the Hedgehog, you play through a series of levels with multiple objectives in each. The next stage/level is determined by which objective you choose to complete in your current level.
For example, if you complete the "hero" objective in "Westopolis" you then move to the stage, "Lethal Highway".
The possible stages and their connections are shown in the image. Note that you can only move from one column to the next, meaning there will always be 6 stages and a final boss per game, no matter which path you take.
The ending (or "last story") of the game is unlocked after beating each of the final bosses in the "boss" column. But interestingly, the game has a unique name for every possible path you can take from stage 1 to the final boss, and every time you complete a unique path, it adds it to a list of your previous games.
How can you find out the number of unique possible paths through this tree?
For example, if you complete the "hero" objective in "Westopolis" you then move to the stage, "Lethal Highway".
The possible stages and their connections are shown in the image. Note that you can only move from one column to the next, meaning there will always be 6 stages and a final boss per game, no matter which path you take.
The ending (or "last story") of the game is unlocked after beating each of the final bosses in the "boss" column. But interestingly, the game has a unique name for every possible path you can take from stage 1 to the final boss, and every time you complete a unique path, it adds it to a list of your previous games.
How can you find out the number of unique possible paths through this tree?
