Types and Variations

Slither Link

March 30, 2006
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Slither LinkSlither Link is a nikoli puzzle sometimes called “Fences.” Slither Link puzzles consist of a field of points in a square grid with numbers inside some of the individual squares. The goal is to connect the points to form a single loop with the constraint that each number must be enclosed on as many sides as indicated by the number. There’s a nice flash tutorial for the puzzle on the nikoli site.

I bring this up because I just came across a great collection of Slither Link puzzles through Passion For Puzzles. Also, if you’re looking for an interesting variation on Slither Link, check out last year’s US Puzzle Championship test. There’s a puzzle called “False Field Fences.” Numbers inside the loop tell the correct number of enclosed sides, while numbers outside the loop indicate an incorrect number of enclosed sides. Of course, before you solve the puzzle, you don’t know which are on the inside and which are on the outside.

Sudoku methods

March 25, 2006
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DJApe has been posting a series of sudoku solving techniques. On the blog, the post are a little bit out of the order that I would recommend, so I’ve rearranged them a little bit. Here they are, 3 steps to mastering sudoku courtesy of DJApe.

  1. Classic Techniques
  2. X-Wing Technique
  3. Swordfish Technique

Enjoy!

Sudoku for programmers

March 23, 2006
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Blogger James has started a sourceforge project called “Project All About Sudoku.” His goal is to create a Java platform for which Sudoku-loving coders can create plugins. He suggests that plugins could include a sudoku creator, solver, or teacher. He freely admits that there are plenty of open source sudoku projects out there (and he’s right), what he’s hoping to do is bring them all to same Java platform. Of course, this is a monumental task but not a bad one. his biggest obstacle will be getting the word out about his project.

Conslide puzzles

March 16, 2006
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From Passion for Puzzles, a new type of sliding block puzzle (in the style of traffic jam puzzles) called conslide puzzles. The key twist here is that two blocks may be connected by a bar that requires them to move together. The bars are raised to different heights so that they can pass over or under each other. It’s been implemented in flash over at puzzlebeast. The goal is to move the red block to the top left corner. It’s pretty challenging and a nice twist on a standard puzzle.

Heyawake

March 1, 2006
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I just found a collection of Heyawake puzzles, so I figured it would be a good puzzle to profile next. Heyawake is also called “divided rooms.” Like Mochikoro, Heyawake is a binary-determination logic puzzle where the goal is to determine which blocks in a grid are filled in and which aren’t. Unlike Mochikoro, Heyawake has a nice wikipedia page.

In Heyawake, the grid is subdivided into rectangular “rooms.” Some rooms have a number in the corner to indicate how many squares should be filled in for that room. Of course, there are a series of rules governing how the squares should be filled in, otherwise it wouldn’t be a puzzle. From the wikipedia site:

  • Rule 1: Painted cells may never be orthogonally connected (they may not share a side, although they can touch diagonally).
  • Rule 2: All white cells must be interconnected (form a single polyomino).
  • Rule 3: A number indicates exactly how many painted cells there must be in that particular room.
  • Rule 4: A room which has no number may contain any number of painted cells (including the possibility of zero cells).
  • Rule 5: Where a straight (orthogonal) line of connected white cells is formed, it must not pass through more than two rooms—in other words, any such line of white cells which connects three or more rooms is forbidden.

The aforementioned collection has plenty of puzzles of varying difficulty. It also has a nice example, in case someone is having trouble with the rules.

Online Puzzles

February 27, 2006
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There always seems to be more and more of these popping up, so I guess they deserve a mention.

Online puzzles are web-based puzzle games where solving puzzles leads you through a series of web pages. For each page in an online puzzle, the goal is “to get to the next page” but how exactly you manage to do that varies from page to page. Often you will have to click somewhere on the page and then enter a password, but you’re just as likely to have to enter a new URL suggested by the puzzle on the page. Often, you will have to look at the page source or find a hidden file. The challenge of the puzzles, more than anything else, is figuring out what exactly you have to do.

I think the most famous example of this game is notpron, which I played for a few screens. Then I reached a screen that seemed to want me to use a program that comes with Windows, and well… I’m not a Windows user and that was that.

There are dozens of this kind of game on the internet now. Most of them are trying to get a piece of the success of notpron. You can find a good list on the wikipedia page.

Kakuro – Cross Sum

February 19, 2006
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kakuroI was at a book store Friday night and noticed a few kakuro books nestled into a display of sudoku related books. It looks like publishers are thinking that the current popularity of sudoku can help them sell book about another puzzle with a Japanese name.

Of course, kakuro (or cross-sum) puzzles aren’t new, but the buzz about them in the US has only risen very recently. Major web sites related to kakuro have shown up in the past six months, and it’s not hard to find blogs that discuss the puzzles and how to solve them.

I’ve often heard sudoku called a number crossword, which seemd odd too me since a sudoku is nothing like a crossword. There are, however, many similarites between crosswords and kakuro. A kakuro grid more closely resembles an American crossword grid. In a crossword, you are given a clue and the answer is limitted by how many blocks are available and by intersecting answers. Likewise with kakuro, you must find digits that sum to a specific value but you are limitted by the number of spaces and the intersecting sums. Additionally, no sum can contain the same digit twice.

It’ll be interesting to see if kakuro can become as big as sudoku and, if it does, what other kinds of puzzles will become popular after it.

Image from wikipedia.

Mochikoro

February 17, 2006
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At some point I will want to go through this list of Japanese puzzles on wikipedia and do a write up for all of them. For right now, I will write them up as I encounter them.

I found this blog recently that contains a few examples of a puzzle called “Mochikoro.” It’s nearly impossible to find any english web sites that feature this puzzle or have descriptions of it. In fact, at the time of this writing, neither wikipedia nor the blog I linked above has any description of the puzzle or instructions on how to solve one.

Fortunately, the blog does contain a link to a page where the puzzle is called “Archipelago” and instructions for solving are included.

The basic idea is to think of the puzzle space as made up of blocks which are either water and land. The numbered squares are land squares and are part of a rectancular island of land that contains the number of blocks indicated by the number. No 2X2 pools of water can exist in the puzzle space and all islands must be joined together diagonally into an archipelago (hence the english name.)

If you’re interested, click over to the blog and try one out. In the meantime, I might write up a wikipedia entry.

Mochikoro

Image copyright 2005-6 Adam R. Wood

Sudoku variant: Mystery Godoku

February 13, 2006
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On the blog for Hidden Staircase Mystery Books, I came across yet another sudoku variant. HSMB’s “godoku” uses letters instead of numbers (a standard variant that I mentioned yesterday) and the letters can be rearranged to form the answer to a clue (in this case a mystery novel) that will fill one row or column.

The clues on this site are all mystery themed, but the theme can be whatever you want. And you don’t need to get the clue to solve the sudoku. They have a new puzzle up now, as well as archives of past puzzles.

Sudoku variations

February 12, 2006
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I started solving sudokus regularly last summer and, little did I know then, I was jumping on a growing trend. Recently, I’ve been scouring the web for sudoku variations, two of which I had encountered in the US Puzzle Championship test. The best article I can find on the topic is one from the Mathematics Association of America which pretty much covers the range of sudoku variations I’ve seen. The article doesn’t have many sample puzzles below, so I’ll comment on the variations below and link to some puzzles you can try.

There are a few obvious ways to change a sudoku puzzle:

  1. Change the grid. Either change the size (e.g. the super sudoku found through this blog) or change the shape of the internal blocks (e.g. the jigsaw sudoku).
  2. Provide more information about which number goes in which square (e.g. the even-odd sudoku found on the World Sudoku Championship test or the greater-than sudoku). The advantage of these kinds of sudokus is that fewer numbers need to be filled in at the start, if any at all.
  3. Put something other than numbers in the individual squares. This can be a straight substitution of other symbols for the digits, like the hamster sudoku. The more ingenious variations mentioned in the MAA article include using digital clock numbers or dice pip numbers. The advantage in these cases is that entire numbers need not be taken away. You can take away inidvidual dice pips or sections of digital clock numbers. It’s another way to provide more limitted information.

The MAA article ends by suggesting some other possible variations that have not yet been devised, including a chess sudoku that would be very interesting.