Free Printable Magic Squares
Print magic square puzzles to fill in. In a finished square, any row, any column and either diagonal reaches one and the same total, known as the magic sum; a few numbers are printed, and the blanks come out one by one through addition and subtraction.
The 3x3 sets open with the ancient Lo Shu square, built from the numbers 1 to 9 around a total of 15, then climb to numbers as high as 30 and as high as 100. The 4x4 sets use the numbers 1 to 16, or larger numbers with a fresh total on every grid. Each set prints one, four or six grids on a sheet, shows the total as a hint on some pages, and comes with a workbook that binds its pages together.
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Last updated on Tue, 03 Nov 2026 01:24:02 GMT
About the magic square puzzles
What makes a square magic
In a magic square, the numbers are arranged so that its lines, across, down and from corner to corner, all give one total, the magic sum. A 3x3 square has eight such lines and a 4x4 square has ten. When a square holds every whole number from 1 to its count of cells, the total is set in advance: 15 for a 3x3 grid of 1 to 9, and 34 for a 4x4 grid of 1 to 16.
How to fill in the blanks
Begin with the total. When it is printed under the square, it is given; otherwise, add the numbers of a line that is already full. Next, spot a line short of a single number: the total minus the numbers in place reveals it. Each number written finishes other lines in turn, until no blank remains, and a last pass over every line catches any slip.
Which set to start with
The Lo Shu sheets come first, with small numbers and four blanks per square. Squares whose numbers reach 30 or 100 keep the same grid but call for larger sums and differences. The 4x4 sheets follow, with more lines to track and six or seven blanks. A single square per page gives big cells for young children or for a board; four or six per page make a practice set for a lesson or for homework.
A puzzle with a long history
Chinese legend tells of a turtle that rose from the Luo River with a pattern of dots on its shell, the Lo Shu square. In 1514, the German artist Albrecht Dürer engraved a 4x4 magic square in his print Melencolia I, and Benjamin Franklin later built 8x8 and 16x16 squares of his own. There is just one 3x3 square of the numbers 1 to 9, seen turned or flipped, but 880 different 4x4 squares of the numbers 1 to 16.
