Archive for August, 2009

Hashi 4-way puzzle

I’ve been on holiday, so sorry for the lack of posts.  But, very quickly, here’s a 4-way Hashi for you!  Connect no more than 4 bridges between any pair of horizontally or vertically neighbouring islands.

Good luck!

Hashi-3 12×12 puzzle
Hashi-3 example solution

I’ve been discussing Hashi variations in the comments to a previous posting, so I thought I’d try out one of them today.  This is not a brand new variation because it’s a somewhat obvious change, but it’s not very commonly seen even so.

In this version of Hashi you must place no more than 3 lines between any two islands (as opposed to the restriction to no more than 2 lines in regular Hashi).  The full rules, then, are:

• Each circle represents an island.  You must draw bridges between islands to connect all of the islands together, so you can travel from any given island to any other island just by crossing bridges.
• Bridges can only be placed in exactly horizontal or vertical directions
• Bridges cannot cross over any islands – when they reach an island they must stop
• Each island must have the number of bridges connected to it specified by the number on the island
• There can be no more than 3 direct bridges between any 2 islands.

Take a look at the example puzzle, which shows how Hashi-3 (anyone got a suggestion for a better name?!) works.

This puzzle is difficult – it will probably take  you a good 15 minutes, despite its size – but see how you find it!

Hashi 30×20 moderate puzzle

Larger puzzles tend to be a bit trickier just because there are more places to look at, so I thought a moderate-rated 30×20 Hashi puzzle could be interesting.  You can of course make Hashi puzzles as large as you like, but the problem is keeping them fun by mixing in difficult parts with easier parts (as this 30×20 might possibly demonstrate!).

The rules of Hashi are pretty simple – check back a few days for full instructions and an example puzzle.

Good luck!

Hashi 15×15 Tricky puzzle

Following up Friday’s first Hashi puzzle here, I thought I’d post a somewhat trickier example.  It’s fairly straightforward until you’re nearly finished, then you’ll have to think just a little bit to complete the puzzle.

For full instructions, please see my previous post.

Good luck!

Hashi 20×20 Easy Puzzle

I haven’t posted a Hashi (aka Bridges) puzzle before, partially because until yesterday I had never got round to writing a program to draw the PDFs – and drawing them out in Illustrator is a little bit time-consuming, so I had kept my Hashi production to the bare minimum.  But now I’ve changed that, having automated much more of the process.  And so here’s the first result of that, an easy (albeit quite large) Hashi puzzle to start the ship sailing (or ball rolling or whatever your metaphor of choice is).

This puzzle is interchangeably called either by its Japanese name of Hashi or Hashiwokakero, or by its Western name of Bridges.  It’s probably easier to give an overview of what you have to do using the Bridges metaphor (it’s clearly a day for metaphors):

• Each circle represents an island.  You must draw bridges between islands to connect all of the islands together, so you can travel from any given island to any other island just by crossing bridges.
• Bridges can only be placed in exactly horizontal or vertical directions
• Bridges cannot cross over any islands – when they reach an island they must stop
• Each island must have the number of bridges connected to it specified by the number on the island
• There can be no more than 2 direct bridges between any 2 islands.

Example Hashi solution

So for example a ‘4′ island in a corner would have to have 2 bridges travelling away from it on each of the two sides it can connect, and two ‘1′ islands next to one another could not connect because they would then be isolated from the rest of the islands.

I’ve included a small example solution here too, so take a look at that if the rules aren’t entirely clear.

Hashi itself is generally relatively easy compared to many other Japanese puzzles, although it is possible to make large puzzles which are pretty tricky – working out how areas are isolated, and must force other bridges, can be quite complex.  But by and large the puzzles are pretty straightforward, as perhaps you’ll find with today’s (admittedly rated ‘easy’) puzzle.

Good luck!