Masyu

An unsolved Masyu puzzle.

Solution to the above Masyu example.

Masyu (ましゅ, Mashu, IPA [maɕu͍]) is a type of path-drawing logic puzzle designed and published by Nikoli. It is played on a rectangular grid of squares, some of which contain circles that are either "white" (empty) or "black" (filled). The goal is to draw a single continuous non-intersecting loop that properly passes through all circled cells.

Background

The puzzle type was originally called Shiroshinju Kuroshinju (白真珠黒真珠 "White Pearls, Black Pearls") and first appeared in Puzzle Communication Nikoli #90. It was invented by in 2000 by アセトニトリル ("Acetonitril"), who introduced the black pearl clues from the earlier puzzle genre "真珠の首飾り" ("Pearl earring") by 矢野龍王 ("Yano Ryuoh") which only contained white pearls. The name Masyu reportedly derives from a misreading of the kanji for "pearl" (真珠 shinju) by Nikoli's president; the name caught on and was made the official name in Puzzle Communication Nikoli #103.

One particular construction of Masyu, known as "Ura-Masyu", places a heavy constraint on the constructor - the puzzle must be uniquely solvable both normally and when all of the pearls switch colors (from white to black and vice versa).

Puzzle Applications

Masyu within a puzzle can be identified from the presence of a grid of squares, some of which filled with black and white circles. As this logic puzzle is one of the more common standard grid puzzles, many puzzlehunt puzzles often directly state its use or provide the rules as plaintext within the puzzle.

The goal of Masyu is to draw a single continuous non-intersecting loop that satisfies the following properties.

• It must pass through every circle.
• The loop cannot turn on a white circle, but must turn on at least one of the adjacent cells in its path.
• The loop must turn on a black circle, but cannot turn on either of the adjacent cells in its path.

In puzzles where the presence of Masyu isn't directly called out, it is very commonly clued in flavortext using the erroneous translation "evil influence" (derived from a literal translation of the unrelated Japanese term 魔手, also pronounced mashu).

Puzzlehunts often feature standard logic puzzle genres presented in unorthodox ways; as such, a puzzle may present a variant on the standard Masyu, changing the grid or tweaking the rules in a manner that creates a completely different puzzle with different deductions to be made.

Strategy

TO DO

Deductions for a standard Masyu mostly revolve around its two types of circles and how they behave with respect to other circles, the edge of the grid, and extant sections of the loop. Below are some deductions that can be done right from the start.

• Black circles touching the edge of the grid (or are one square away from touching the grid) must have one line going away from the side.
• White circles touching the edge of the grid must have the line going parallel to the side.
• Two black circles adjacent to each other must have two lines on the line segment going away from each other.
• Two white circles in a row either have two lines going through them in parallel or a single line going through them that turns upon leaving either circle.
• Three or more white circles in a row must have multiple lines going through them in parallel.

Some of the initial deductions can cause some options for black circles and white circles to violate the loop requirement, allowing for more deductions to be made.

Notable Examples

Played Straight

• Sleeping Beauty Meta (MITMH 2016) (web) - The meta for the Sleeping Beauty round, Masyu is clued using the "Evil Influence" cluing.
• Refreshment Stand (Puzzle Rojak) (web) - This variant of Masyu involves nine loops instead of one.

Notable Twists

• Oyster Card (MITMH 2014) (web) - Masyu, with the additional twist that it's played on a map of the London Underground.
• RED SUS (Silph Puzzle Hunt 2021) (web) - The lines of this Masyu are not axis-parallel.

See Also

• Puzzles that involve Masyu
• Masyu puzzles on puzz.link