Short answer: How do you solve a hashi (bridges) puzzle?
Hashi, also called Bridges or Hashiwokakero, is a Nikoli logic puzzle. Join numbered islands with straight bridges, across or up and down, so each island has as many bridges as its number. No more than two bridges join a pair, bridges never cross, and all islands link into one group. Start with one-neighbor islands.
Hashi looks like a page of scattered numbered circles. Once you know the four rules, it plays a lot like sudoku: you look for a move that has to be true, and that move unlocks the next. You only need to count to 8.
What are the rules of hashi?
Each circle is an island with a number from 1 to 8. You draw bridges between islands. Nikoli, the Japanese puzzle publisher behind the game, gives these rules (Nikoli: Hashiwokakero):
Each island gets as many bridges as its number. A 3 has exactly three bridges touching it.
No more than two bridges join the same two islands. Draw a double bridge as two parallel lines.
Bridges never cross each other or pass over an island.
Every island links into one group. You must be able to travel from any island to any other.
Bridges run in straight lines, across or up and down, never diagonally (Wikipedia: Hashiwokakero). The puzzle is also published as Bridges, and in The Times as Hashi.
How do you start a hashi puzzle?
Look for islands with no choice. Count the neighbors an island can reach in a straight line (up, down, left, right, with nothing in the way), and remember each neighbor can take at most two bridges from it.
An island with only one neighbor sends all its bridges to that neighbor. A 2 with one neighbor gets a double bridge.
A full house: if the number is twice the neighbors it can reach, every neighbor gets a double bridge. That means a 4 with two neighbors (often in a corner), a 6 with three, or an 8 with four.
One short of full: a 3 with two neighbors, a 5 with three or a 7 with four needs at least one bridge to every neighbor it can reach. Draw those single bridges now.
Two 1s never join each other, unless they are the only two islands. Joined, they would be finished and cut off from everything else. The same goes for two 2s joined by a double bridge.
After each bridge, cross off or shade any island that is complete. Wikipedia notes this is common practice, and it shows you which islands are still open.
What do you do when you get stuck?
Recount the islands that are partly done. A bridge you drew may have blocked another island's path, which can leave it only one direction.
Check the one-group rule. If a bridge would close off a small group of islands with nothing left to connect, that bridge is wrong.
Work in pencil. Draw a bridge only when you are sure, and erase cleanly if you made a mistake.
A well-made hashi has exactly one solution, so you should never need a blind guess.
What makes a hashi puzzle harder?
Bigger grids and more islands mean more to keep track of. The kind of step a puzzle needs matters more than its size, though. In our book, levels are set this way:
Easy and Medium can be solved with counting steps alone, like the starting moves above.
Hard puzzles need at least one "don't cut off a group" step, such as refusing to join two 1s.
Very hard puzzles need at least one "test it" step: suppose a bridge, follow the counting and cut-off steps, and if that leads to something impossible, the bridge goes the other way.
If a book's hard puzzles feel like guessing, the levels may have been set by grid size alone.
How do you print hashi puzzles so they stay easy to read?
APH VisionAware says 18 point is the standard size for large print, and that bold black print on a matte white or cream background is easiest to read (APH VisionAware: Reading with Low Vision). For hashi:
Island numbers well above 18 point and one puzzle per page leave room to draw neat double bridges.
Print at "Actual size" or 100%. "Fit to page" can shrink the grid.
Use matte copy paper rather than glossy, to cut glare.
Print one page at a time if you like to start over. A clean copy is easier than erasing a tangle of lines.
Keep the answer pages apart so a glance does not spoil the next puzzle.
If you already like large-print sudoku, see our sudoku guide for picking levels.
If you want a stack ready to print: Slow Coffee Hashi is a 408-page US Letter PDF with 250 puzzles, one per page. Part 1 has 100 large-print puzzles (30 Easy, 30 Medium, 25 Hard, 15 Very hard) with island numbers 21 point or larger. Part 2 has 150 more on bigger grids, up to 14 by 14. It includes how-to-play pages, a worked example solved step by step, and every answer, and each puzzle page tells you where its answer is. A computer solver set each level from the steps it needs, and a second, separate program confirmed every puzzle has exactly one solution. It's for personal and classroom use. $3.99 on Gumroad or Etsy.
General information. Hashi is a puzzle for enjoyment. It is not a medical product and does not diagnose, treat or prevent any condition. Talk to an eye doctor or low-vision specialist about your own vision.