How to Play Magic Square
Overview
A Magic Square is an ancient mathematical puzzle dating back over 4,000 years. It consists of a grid where you arrange consecutive numbers so that every row, every column, and both main diagonals all sum to the same number - the magic constant. For a 4×4 grid using numbers 1-16, the magic constant is always 34.
Video Tutorial
Rules
- 1Use each number from 1 to 16 exactly once in the 4×4 grid.
- 2Each row must sum to 34 (the magic constant).
- 3Each column must sum to 34.
- 4Both main diagonals must sum to 34.
- 5Gray cells contain prefilled numbers and cannot be changed.
The Magic Constant
The magic constant for an n×n magic square using numbers 1 to n² is calculated as:
Controls
Solving Strategies
Use the Sums
If a row or column has only one empty cell, calculate what number is needed: 34 minus the sum of existing numbers.
Check Diagonals First
Diagonals have the fewest cells (only 4), so they're often the most constrained. Start by looking at diagonal possibilities.
Complementary Pairs
Numbers that sum to 17 (like 1+16, 2+15, 8+9) are complementary pairs. In a 4×4 magic square, opposite cells often contain these pairs.
Process of Elimination
Keep track of which numbers are already placed. If a cell can only fit one remaining number based on sum constraints, that's your answer.
Trial and Error
Sometimes you need to try a number and see if it leads to a valid solution. Use undo if it doesn't work out!
History
The earliest known magic square is the Lo Shu Square from ancient China (around 2200 BCE). Legend says it was revealed on the back of a turtle emerging from the Lo River. Magic squares have fascinated mathematicians, artists (like Albrecht Dürer), and mystics for millennia. Benjamin Franklin famously created intricate magic squares as a mental exercise.