Re-Shuffling Rush Hour

A sliding block puzzle is normally played inside a tray, in which the block can move around orthogonally. How about other possibilities of moving block around? Enter Subway Shuffle: Rush Hour on a graph. Or, as the developer Bob Hearn explains it:

Imagine playing Rush Hour, but make all the cars 1×1 instead of 1×2 or 1×3. But still some can only move vertically, others horizontally. Replace the cars by tokens, red for horizontal, blue for vertical, and put the tokens on nodes of a graph with colored edges: red tokens can only move on red edges, blue on blue. If you use a grid graph, with horizontal edges red and vertical edges blue, then you have 1×1 Rush Hour. If you relax the grid graph constraint, and also allow more colors, then you get Subway Shuffle. These relaxations allow for lots of interesting possibilities in puzzle configuration. It’s also possible to have extremely complicated puzzles in a very small space: I’ve generated some puzzles on small graphs that require over 1,000 moves.

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Know How to extend Rush Hour

Things move fast in the app store. I just wrote this summary on Rush Hour puzzles, and then today a new variation becomes available: Know How [iTunes Link]. I have not bought the game (at 3€ I find it too expensive to try it out; hopefully a lite version will become available soon). However, from the description and the other information on the web it is clearly a Rush Hour variant. The block can only slide in the direction of the elongation, and the treasure box has to be moved out to a destination outside the playing field (at the bottom in the screen shot to the right).

Rush Hour

One approach to make sliding block puzzles more complicated is by restricting the movements of the blocks. The most prominent example of this strategy is Rush Hour. In this puzzle, all sliding blocks are rectangles of size nx1. These blocks can only be moved in the direction of the elongation. The original trick to make this restriction transparent to the user is to show the block as cars (hence the name “Rush Hour”). It is then immediately obvious that the car can only be moved forwards or backwards, and not sideways.

Rush hour was invented by Nobuyuki “Nob” Yoshigahara and marketed as a physical puzzle by ThinkFun (formerly Binary Arts). There are at least four implementations of Rush Hour available in the app store (links redirect to iTunes):