A Magic Square Puzzle is typically a grid of nine squares where a given sequence of numbers must be placed in a specific order to equal another number in all directions. Somewhat similar to a 15 Puzzle, depending on the mechanics, though a magic square usually has complete freedom of moving pieces if it has physical pieces for each number.
Often used in room escape point-and-click games. Sometimes you have to go on a Pixel Hunt to collect all the numbers before you can start work on the puzzle.
Sub-Trope of Grid Puzzle, the general trope for puzzles solved by arranging the elements of a grid. Compare Crossword Puzzle (using clues to fill words into overlapping horizontal and vertical lines), Match-Three Game (a puzzle requiring matching three objects that are similar in some way), and Queens Puzzle (putting eight queens on a chessboard so they can't capture each other).
Magic squares in general tend to be Numerological Motifs.
Examples:
Alternate Reality Games
- Perplex City: There's a card with a 4×4 magic square which must be filled in, with only two starting numbers.
Anime & Manga
- Phi-Brain: Puzzle of God: The third episode features one.
- Spiral: This is one of the puzzles the Blade Children pull out to test Ayumu. He has to solve a magic square puzzle by tapping each square in order to stop a bomb from exploding in a crowded concert hall while Hiyono holds onto a rod to give him time to solve it, preventing her from escaping to safety. Trick is—he has to notice it was a magic square all on his own.
Literature
- Masquerade (1979): The "penny-pockets lady" in the fourth illustration has a 4x4 magic square hanging from her belt; the numbers are in the same arrangement as in the magic square in Albrecht Dürer's 1514 engraving Melencolia I, but with an empty space where the 7 should be. It doubles as one of the most important clues to how to solve the book's main riddle thanks to the correspondence between its numbers and the colours and letters on the paper on the wall in the twelfth illustration, and the numbers in the grid in the sand in the last illustration.^{How so? }
- Siege of Sardath: You need to play one of these at one point in order to get a secret number.
Live-Action TV
- Stargate Atlantis: "The Brotherhood" is all about this puzzle. First version, the eight pieces of movable numbers are arranged in a grid square over a wide area of land. In the final puzzle, nine pieces with the numbers 1-9 were placed. One piece fits into a certain slot in the middle of the grid, and the eight others were placed around it. After witnessing one Mook get killed by an incorrect arrangement, Sheppard solves the puzzle by realizing that the numbers 1-9 can be placed in a grid to add up to 15 in all directions. Of course, there's a certain element of Fridge Logic to the fact that quite a few different such arrangements are possible, but one can Hand Wave this by claiming that any of them would have worked.
Non-Fiction
- The World Almanac For Kids: Most issues present a handful of magic squares with the rules explained for kids to solve.
Video Games
- Dr. Brain: Castle of Dr. Brain and Island of Dr. Brain have magic squares as one of the puzzles in each game. In the first game, the puzzle is the same every time you play (with a blank board), but the size will differ based on the difficulty. In the second game, you can replay the puzzle as many times as you like, and have it randomised each time.
- Genshin Impact: The second step to solving Watatsumi Island's "8 cubes" puzzle is realizing that the number of floating stone slates on each stone has to be arranged to sum the same number.
- Might and Magic: The first game has a 4×4 magic square dungeon, the successful solution of which will grant your party +2 intelligence.
- Onimusha 2: Samurai's Destiny: You have to solve a magic square puzzle to open the chests containing the proper trinket twice.
- Pokémon Reborn: In fake Devon Corp, there's a 6×3 magic square that has Thunderbolt, Gardevoirite, and Darkinium-Z as rewards. It also provides a password you can tell Agathe City woman in exchange for a Manectrite and a Department Store Sticket.
- Professor Layton and the Curious Village: It should not surprise anyone that this game has one of these.
- Safe Cracker: Its 2006 spiritual successor includes a 3×3 magic square grid in a trio of puzzles built into an elaborate mechanical contraption, which extends with each puzzle solved until it reaches the ceiling of the museum.
- Shadow Hearts: From The New World: The first test you must complete to get one of Johnny's Tools is a staggered magic square, requiring you to match different sums for each direction.
- Sherlock Holmes: Secret of the Silver Earring: The PC version has an unusually large one, ten columns wide.
Visual Novels
- Fatal Hearts: This is one of the puzzles, complete with a fun history lesson (tm).
- Nine Hours, Nine Persons, Nine Doors: There's a 3×3 square that must be filled with the numbered pins you find in the Cargo room. If it wasn't difficult enough per se, part of its nastiness comes from figuring out what the rows, columns, and diagonals must equal. It gives you a hint in hexadecimal, though, which is a numerical base you've been using in previous puzzles; but you might as well have forgotten about it by the time you encounter this square, especially due to New Game Plus reruns.
Web Videos
- Numberphile: Matt's rather terrible quasi-solution to a magic square involves reusing two numbers and, even then, there's one diagonal with the wrong sum. This, and all of his future flawed solutions, are called the "Parker Square".^{note }