Futoshiki - Logic Puzzle Game

Futoshiki (Japanese for “inequality”) is a challenging and engaging logic puzzle game. The goal is to fill a square grid with numbers such that every row and column contains each number exactly once, while also obeying the inequality signs (greater than and less than) placed between some of the squares.

The Objective

The primary goal of Futoshiki is to completely fill the grid with numbers ranging from 1 to the size of the grid (for example, 1 to 5 in a 5x5 grid). You must satisfy two main types of constraints: the uniqueness of numbers in rows and columns, and the relational symbols placed between adjacent cells.

The Tools You Have

Before starting, it’s helpful to understand what you’re working with:

The Grid: A square grid of varying sizes (commonly 4x4, 5x5, 6x6, etc.).
Given Numbers: Some cells may already be filled with numbers to get you started.
Inequality Signs: Greater-than (>) and less-than (<) symbols are placed between certain adjacent cells (both horizontally and vertically).

The Rules to Follow

Futoshiki has a few simple but strict rules:

Row Uniqueness: Every number from 1 to the grid’s size must appear exactly once in each row.
Column Uniqueness: Every number from 1 to the grid’s size must appear exactly once in each column.
Inequalities: The numbers placed in adjacent cells must satisfy any inequality signs between them. For instance, if you have Cell A < Cell B, the number in Cell A must be strictly smaller than the number in Cell B.

Simple Strategy

Futoshiki is a puzzle of deduction and logic. Here’s a simple strategy to get you started:

Look for Extremes: If a cell is surrounded by “greater than” signs, it must contain a large number. Conversely, if it is surrounded by “less than” signs, it must be a small number. For example, in a 5x5 grid, a cell that must be greater than another cell cannot be a 1, and a cell that must be smaller than another cannot be a 5.
Chains of Inequalities: Follow chains of signs (e.g., A < B < C). These chains severely restrict the possible numbers for those cells.
Use the Process of Elimination: Keep track of the numbers already placed in each row and column. This helps you figure out the remaining possibilities for empty cells.
Cross-Reference: Combine the knowledge of what numbers are missing in a row/column with the inequality constraints to force a specific number into a cell.

Example of Play

Imagine you have a 5x5 grid. You have an empty cell that has a < sign pointing to a cell containing a 2.

Since the empty cell must be strictly smaller than 2, and the only number smaller than 2 in a 1-5 range is 1, you know the empty cell must contain a 1.

Tips for Beginners

Start by scanning the board for long chains of inequalities or given numbers that severely limit their neighbors.
Pencil in possibilities if you are unsure, and use deduction to eliminate them.
Don’t rush; make sure every placement doesn’t violate any rules in its row, column, or adjacent inequalities.

Have fun solving the puzzle!