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1. In addition to reducing mistakes, this can also help locate potential "short circuits": keeping in mind that all islands must be connected by one network of bridges, a bridge that would create a closed network that no further bridges could be added to can only be permitted if it immediately yields the solution to the complete puzzle.

2. In Hashiwokakero(hashi, chopsticks, bridges) you are the king of the islands, and your job is to connect the islands according to their populations – small islands need only one bridge (it says 1 in the island), and larger islands need more bridges (the number in the island).

3. The simplest example of this is two islands showing '1' aligned with each other; unless they are the only two islands in the puzzle, they cannot be connected by a bridge, as that would complete a network that cannot be added to, and would therefore force those two islands to be unreachable by any others.

4. Solving a Hashiwokakero puzzle is a matter of procedural force: having determined where a bridge must be placed, placing it there can eliminate other possible places for bridges, forcing the placement of another bridge, and so on.

5. An island showing '3' in a corner, '5' along the outside edge, or '7' anywhere must have at least one bridge radiating from it in each valid direction, for if one direction did not have a bridge, even if all other directions sported two bridges, not enough will have been placed.

6. Connect islands (the circles with numbers) with as many bridges as the number in the island.

7. This can be generalized as added bridges obstruct routes: a '3' that can only be travelled from vertically must have at least one bridge each for up and down, for example.

8. Any bridge that would completely isolate a group of islands from another group would not be permitted, as one would then have two groups of islands that could not connect.

9. Bridges cannot go across islands or other bridges.

10. It is common practice to cross off or fill in islands whose bridge quota has been reached.

11. The bridges will form a continuous link between all the islands.