Hashi logic,
minus the guesswork.

What are the main hashi puzzle techniques?

Most hashi puzzles fall to four moves: double every bridge on a full island, place one bridge to each neighbour under the one-less rule, give an only-neighbour island everything it needs, and avoid isolating pairs of small islands. Everything else is counting what is left and checking for crossings.

Hashi rewards counting, never guessing.

A worked hashi solve, step by step

A 5 by 5 board with eight islands and exactly one solution. Each step names the technique it uses.

1. Step 1

   Full island in a corner

   A is a 4 in a corner with only two neighbours, B and C. Four bridges over two neighbours means a double to each. B's 2 is now complete.

2. Step 2

   The same move, twice

   G is also a 4 in a corner with two neighbours, D and H. Double bridges to both.

3. Step 3

   Count what is left

   H needs 4. G already gave 2, and its only other neighbour is F, so H to F is a double.

4. Step 4

   Only one neighbour

   E is a 2 that can only see F. Whatever E needs must come from F: a double. F now has 2 + 2 = 4, done.

5. Step 5

   Finish by subtraction

   C needs 3 and has 2 from A. Its only open neighbour is D, so one single bridge. D now has 1 + 2 = 3.

6. Step 6

   Connectivity check

   Every island is complete and you can travel from any island to any other along bridges. One connected group: solved.

Hashi techniques glossary: 10 terms

• Island
  A circled number. The number is how many bridge lines must touch it in total.
• Bridge and double bridge
  A straight horizontal or vertical line between two islands. Two islands can share at most two bridges.
• No-crossing rule
  Bridges may not cross other bridges or pass over islands. One bridge can quietly block another option.
• Connectivity rule
  When finished, every island must be reachable from every other along bridges: one connected group.
• Full island
  An island whose number equals twice its neighbour count: a 4 with two neighbours (usually a corner), a 6 with three (usually an edge), an 8 with four. Every bridge is a double.
• One-less rule
  A 3 with two neighbours, a 5 with three or a 7 with four: at least one bridge to every neighbour is certain.
• Only neighbour
  An island that can see just one other island must take all its bridges from that neighbour.
• Isolation
  Two 1s joined only to each other would form a closed pair, so they cannot be linked when other islands exist. The same goes for a double between two 2s.
• Count what is left
  Subtract the bridges already drawn from an island's number, then look at which neighbours can still accept them.
• Blocking
  Drawing one bridge can cut a line of sight for another pair. Check crossings after every move.

Full island first, one-less second, then count.

How Sumbriska works, in 3 steps

1. Read the targets. Each island shows a target number.
2. Flip a bridge. Tap a bridge and watch both totals change as numbers are sent between the two islands.
3. Land every sum. The board is solved when every island hits its target exactly. Hints, Undo and step explanations never cost XP.

Where hashi habits carry over: starting at the most constrained island, counting what is left after each move, and checking both ends of every bridge you touch.

What the slider shows

The board at the top is the worked example. On the left of the slider you see the islands as the puzzle starts; drag right and the finished bridges appear. Compare the two and the techniques jump out: both left corners and the bottom-right corner are full islands with doubles, E's only neighbour is F, and the single bridge from C to D is the last count.

One design decision we made in Sumbriska, borrowed from the best logic puzzles: help never costs you. Hints, Undo and the step explanations are free to use and don't take XP, so you learn the reasoning instead of avoiding it.