NES Box Art: Final Fantasy 

Final Fantasy is a fantasy role-playing video game developed and published by Square in 1987. It is the first game in Square’s Final Fantasy series, created by Hironobu Sakaguchi. Originally released for the NES, Final Fantasy was remade for several video game consoles. The story follows four youths called the Light Warriors, who each carry one of their world’s four elemental orbs which have been darkened by the four Elemental Fiends. Together, they quest to defeat these evil forces, restore light to the orbs, and save their world.

The game was originally going to be called Fighting Fantasy, but the name was changed to Final Fantasy when the development team discovered Fighting Fantasy was the title of a series of single-player roleplay gamebooks.

Gameplay || Game Wiki

Brooks, Smith, Stone and Tutte discovered the first dissection of a square into smaller squares of pairwise different sizes. Their challenge started with more-or-less trial-and-error and elementary algebra, and resulted in a jungle of squared rectangles.

The quest took a major turn when Smith proposed a diagrammatic way to encode squared rectangles into (planar) graphs, which turned out to be interpretable as electric networks! Assuming wires of unit resistance, both Kirchhoff’s laws are fulfilled:

1) The total incoming current equals the total outgoing current in each central node. This is true because the first sum corresponds to the sides of the squares directly above a certain horizontal segment, and the second sum to the squares directly below the same segment (horizontal compatibility).

2) The oriented sum of the currents in any circuit is zero. This is true because the positive and negative terms correspond to the sides of the squares directly to the left and the right of a certain vertical segment (vertical compatibility).

Using known facts from electrical network theory, they eventually found the first squared square, with 69 smaller squares. This was subsequently improved, until Duijvestijn found the smallest squared square (with 21 squares) and proved its uniqueness, by intensive computer search.

Read more about the adventure here.