Tuesday, March 07, 2006

Alternating Hiroimono

Hiroimono is a puzzle that's been around for centuries in Japan, involving picking up stones on a Go board. It's even appeared in the WPC a few times.

The traditional rules of Hiroimono are:

  1. Choose a stone to start at, and start in any of the four directions.
  2. Your path can only go in the four directions (along the lines).
  3. You can only change directions when you pick up a stone,
    and you cannot go back the way you came when you do so.
  4. You must always pick up a stone when you reach it.

Note that once you pick up a stone, it is gone; you cannot stop there again and change direction.

Scott Kim posted a nice set of Hiroimono puzzles in a previous issue of Discover Magazine.

However, playing this game means that half of your Go set is unused!

So, let's add another rule:

5. You must alternate black and white stones. (Your starting stone can be any color, however.)

With those rules, see if you can solve these four puzzles.





Friday, December 30, 2005

Sets, Supersets, and Hypersets

At the first-ever World Puzzle Championships in New York in 1992, the players were treated to a new puzzle based on a recently-released commercial game called Set(r). The game since then has gone on to become a puzzle-game-player's staple. (Not that there are that many puzzle-game--players out there, though -- I voted it 3rd in my submission to The One Hundred, but it didn't even make the cut.) In the basic game as written, 12 cards are dealt out, and players have to find groups of three cards called a "Set". Three cards are a Set only if they have a certain property. In 1995, I invented a variant of Set called Superset, which was significantly more difficult, and players who were really fast at Set would find this variant like learning Set all over again. I posted the rules on the Internet in 1999.

At the World Puzzle Championship in 2001 in Brno, I played Superset for a few hours with Rodolfo Kurchan. I was surprised to find that after a while, we started getting better at "seeing" Supersets!

That remained the status quo for a while until earlier this year in 2005, when my friend Luke Weisman told me that he
had taught Superset to some friends of his and they had invented a game they called Supersuperset. I took a look at the rules and felt disappointed -- Supersuperset was more difficult than Superset all right, but not substantially so, and it didn't "feel" like the right extension.

So, about after a few hours of doodling and calculation, I came up with the proper extension to Superset, which I call Hyperset.

This month's column will let you explore a little bit of that discovery process. Instead of worrying about color printing (and infringing copyright, for that matter), I'll borrow a trick from Andrew Plotkin and use my own made-up symbols instead of the original sets. Here we go!

This is a Set:

This is also a Set:

Of these four groups of three, one is not a Set. Which one?

This is a Superset:

This is also a Superset:

Of these four groups of four, one is not a Superset. Which one?

This is a Hyperset:

This is also a Hyperset:

Of these four groups of five, one is not a Hyperset. Which one?

Here are ten symbols. Among these ten cards there are hidden nine Supersets and nine Hypersets. Can you find them all?

Tuesday, November 08, 2005

Inverted Number Place

A traditional Number Place (Sudoku) has a 9x9 grid with four thick vertical lines and four thick horizontal lines that divide the grid into nine 3x3 regions.
But what if you made the thick lines thin and the thin lines thick? You might get something like this.

In these four puzzles, the 3x3 regions "wrap around" the edges and corners of the grid. Otherwise, the rules are identical to that of a classic number place puzzle. Have fun!


Welcome to Puzzles Imponderous!

This is where I plan to publish a monthly (or semi-monthly) column on puzzles. The focus of this column is on culture-neutral puzzles, as seen in the World Puzzle Championship -- as much as like word-puzzles and the like, you won't see them here. Why? Because the contents will first appear in Akýl Oyunlarý, a Turkish puzzle magazine run by some friends of mine. So, if you want to see the articles earlier, go ahead and get a subscription from them. You might need to learn Turkish, but trust me, you don't need to to enjoy most of the puzzles.

On the other side, if you have any ideas or suggestions for articles, please feel free to send me an e-mail or comment in the blog!