Inception’s Penrose Staircase

You’re trapped in a dream featuring a Penrose staircase, the impossible architecture that characters grappled with in Inception. You start on the blue step, and you’re allowed eight moves. On each one, you may travel either up or down. If you go up, you move a number of spaces equal to N-1, where N is the number on the step you began the move—6 at the start. If you go down, travel N+1 spaces. At the end of your move, you’ll be on a step with another number. Again, move up or down the stairs following the same rules (N-1 or N+1). Each move must end on an unvisited step. Your goal is to finish where you began—on blue 6.


This level of the dream is far larger in size, and has many more dead ends. You start on the 4 step, and you must visit all 16 steps exactly once each, ending back where you started.


Now you are on the final level of the dream, where staircases rise and fall like imaginary skyscrapers. The movement rules are the same as before, requiring you to visit all 24 steps once each, returning to your starting point. However, once you leave a step, you must either go all up or all down during that particular move. Here there may be many ways to complete the journey, but you may be hard pressed to find even one. Once you have completed this staircase, you may finally exit the dream. That is, assuming you believe that you started in reality….


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