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Game Design Essentials: 20 Real-World Games

August 12, 2010 Article Start Previous Page 20 of 21 Next

19. The Logic Puzzles of Nikoli

Published by Nikoli

Type: Solitaire logic puzzles

Depth: Moderate to High

Designed by: Various creators

Luck factor: None

Description: A sequence of inventive puzzle types published by Japanese puzzle magazine Nikoli. Counted among their number is Sudoku. They are all difficult straight-logic puzzles. Once one knows how to solve a given type, they usually aren't extremely difficult, but figuring out how to do that is an engrossing pastime.

Play Summary

Nikoli is a Japanese puzzle magazine famous for its inventive logic puzzles. It is not the ultimate origin of the puzzle most know as "Sudoku", but it is the original source of its popularity as well as its most popular name. Alongside it in the magazine are a variety of other wonderful logic puzzles of varied types. These puzzles all involve a diagram which must be completed in some way to satisfy an initial state.

In well-made puzzles of the kind, there is only one solution. For easier puzzles it is usually possible to work out the solution using elementary logic. Harder ones require more insight into the implications of the rules, and venture into trial and error. The hardest puzzles usually require experimentation or transcendent insight.

Everyone knows of Sudoku. To represent these puzzles, I chose a less well-known example of the type, a puzzle Nikoli calls Slitherlink. I tend to think of it by the name given to it by Simon Tatham's Puzzle Collection, which is Loopy. Illustrations presented here are from that computer adaptation, but the lessons involved work as well with the paper version. The various logic puzzles Nikoki publishes are varied, but Slitherlink is a good jumping-off point.

Slitherlink involves a grid of points that mark the page off into squares. In the middle of some of the squares are numbers. The solution to the puzzle involves connecting the dots along the invisible grid lines so that it forms a complete loop, with no stray lines, of straight and right-angled line segments. When the puzzle is solved, all of the numbered squares will have exactly that many filled in perimeter line segments. There is only one loop that can be drawn that satisfies these conditions, a fact that, itself, is sometimes a subtle clue.

Look at this unsolved diagram, an "Easy" puzzle made by Simon Tatham's Puzzle Collection. With practice, such a grid can often be completed in three minutes or less. What can we determine about it?

Well first, the 0 squares can have no lines adjacent. Of each of the 3 squares, if we ever discover any adjacent lines are blank, we can rest assured the other three must be filled in. That 3 in the upper-right corner must have its corner lines filled, because either both of those lines must be drawn or neither and 3s permit only one empty border.

Less obviously, adjacent 3s must have the lines between them and on either side of the pair filled in. The line must ultimately prove to be continuous without branches, so in cases where the line bends at a right angle through an intersection, the other two lines coming off it must be empty. These facts, combined with obvious points about 1s and 2s with relevant known lines adjacent, let us get to a state like this:

It is not particularly difficult to finish the whole grid from this point. Harder scenarios require more obscure observations about the nature of the puzzle, rely on using higher-order rules (such as the closed nature of the loop in Slitherlink), and may demand the solver make trial and error experiments.

All of these facts are also true about Sudoku and most of the other Nikoli puzzles. In this way, all of these puzzles are the same kind of thing. Once you learn the tricks to solving one type you can reliably solve up to medium difficulty puzzles of the breed without huge effort. But to get beyond that requires ever-more demanding resources of insight and memory. This is the realm in which expert solvers dwell. Even the best solvers cannot do the hardest Sudoku grids without a lot of work; using special tricks will only take one so far.

What can we draw from this game?

Of particular interest to game developers is the number of these puzzles that have been adapted into successful computer versions. In addition to Sudoku's starring rule as a sideline of Nintendo's Brain Age series, the open-source game Simon Tatham Puzzle Collection collects play modules for many of them, as well as fairly decent random puzzle generators, into a single package.

Lots of inspiration for puzzle games is to be found among the pages of Nikoki. Logic puzzles are extremely popular right now, and a lot of the popularity of Nintendo's Brain Age series probably derives from the excellent Sudoku collection and solving interface included with each of them. In addition, elements of the puzzles might be cannibalized for use as puzzle minigames in other genres.

Further reading:

Nikoli now maintains an English website, with puzzle instructions and puzzles to solve.

For English-speaking audiences, the premiere puzzle periodical has long been Games Magazine, the publication which birthed Will Shortz onto an unsuspecting world. Every issue provides a number of pencil puzzle pages, and usually among them are some of the Nikoli breed.

Article Start Previous Page 20 of 21 Next

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