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Shortest-path puzzles: the idea behind finding the shortest link
A shortest-path puzzle asks for the fewest steps between a start and a goal. Computers solve it with simple, elegant methods; people solve it with knowledge and intuition.
Graphs, in one paragraph
Mathematicians describe connected things as a graph: dots (people, places, brands) joined by lines (real connections). A path is a sequence of lines from one dot to another, and its length is the number of lines it uses. The shortest path is the one with the fewest.
How a computer finds it
When every link counts the same, the standard method is breadth-first search: look at everything one step away, then everything two steps away, and so on, until the goal appears. The first time you reach it, you have a shortest path. When links have different costs, Edsger Dijkstra's algorithm (published in 1959) does the same job by always expanding the cheapest route found so far.
Par: the shortest route you could have found
Like golf, a shortest-path puzzle needs a par: the fewest links that solve it. In CHAINED each chain has a par of 2 or 3, worked out from the cards you can actually be shown, and you have a couple of spare moves on top. Matching par scores full points; every extra link scores a little less.
Why people find it hard (and fun)
A computer sees every connection at once. You do not: you see a few cards and have to guess which one heads toward the goal. The best moves are often the ones that jump between worlds — a musician who starred in a film, a brand that sponsored a team. That is where the surprise, and the learning, comes from. See how to play for the rules in full.