4x4 Magic Square Puzzles

Print large 4x4 magic squares, one to a sheet, and complete them so that the four rows, the four columns and the two diagonals land on the same total. Sixteen cells and ten lines make a bigger challenge than the 3x3 squares, with more numbers to keep in mind.

The first twelve sheets place each whole number from 1 to 16 once, so every line totals 34, with six cells blank. The last twelve use numbers as large as 100, with a new total on each sheet and seven blank cells. Three sheets in each half print the total as a hint. A workbook gathers all twenty-four.

Part of the Magic Squares collection, Last updated on Tue, 03 Nov 2026 01:24:20 GMT.

Free Printables

4x4 Magic Square of Numbers 1 to 16, Sum Given (N1)

A large 4x4 square to complete, built on 1 to 16, with six cells missing, magic sum 34 below. | zuzuzi.com

4x4 Magic Square of Numbers 1 to 16, Sum Given (N2)

4x4 Magic Square of Numbers 1 to 16, Sum Given (N3)

4x4 Magic Square of Numbers 1 to 16 (N4)

A large 4x4 square to complete, built on 1 to 16, with six cells missing. | zuzuzi.com

4x4 Magic Square of Numbers 1 to 16 (N5)

4x4 Magic Square of Numbers 1 to 16 (N6)

4x4 Magic Square of Numbers 1 to 16 (N7)

4x4 Magic Square of Numbers 1 to 16 (N8)

4x4 Magic Square of Numbers 1 to 16 (N9)

4x4 Magic Square of Numbers 1 to 16 (N10)

4x4 Magic Square of Numbers 1 to 16 (N11)

4x4 Magic Square of Numbers 1 to 16 (N12)

4x4 Magic Square of Numbers up to 100, Sum Given (N13)

A large 4x4 square of numbers up to 100 and seven empty cells, its own sum below. | zuzuzi.com

4x4 Magic Square of Numbers up to 100, Sum Given (N14)

4x4 Magic Square of Numbers up to 100, Sum Given (N15)

4x4 Magic Square of Numbers up to 100 (N16)

A large 4x4 square of numbers up to 100 and seven empty cells. | zuzuzi.com

4x4 Magic Square of Numbers up to 100 (N17)

4x4 Magic Square of Numbers up to 100 (N18)

4x4 Magic Square of Numbers up to 100 (N19)

4x4 Magic Square of Numbers up to 100 (N20)

4x4 Magic Square of Numbers up to 100 (N21)

4x4 Magic Square of Numbers up to 100 (N22)

4x4 Magic Square of Numbers up to 100 (N23)

4x4 Magic Square of Numbers up to 100 (N24)

Ten Lines to Balance

A 4x4 square has ten lines, across, down and on its two diagonals, and all of them must give the same total. Each number belongs to two or three of those lines, so a single wrong cell spoils several at once, and checking becomes part of the puzzle.

Dürer’s Famous Square

Albrecht Dürer placed a 4x4 magic square of the numbers 1 to 16 in his engraving Melencolia I, and every line of it totals 34. The two middle cells of its last row hold 15 and 14, which spell out 1514, the year of the print. The sheets built from 1 to 16 make squares of the same family.

Larger Numbers, New Totals

From sheet thirteen on, the numbers grow as large as 100, the total changes from one square to the next, and seven cells are blank instead of six. The solver first adds a complete line to learn the total every other line must reach, then works mostly with two-digit numbers.

Frequently Asked Questions

Why Do the Lines Total 34 With the Numbers 1 to 16?

Taken together, the numbers 1 to 16 make 136. The four rows divide that amount equally, so each row is worth 136 ÷ 4 = 34, and columns and diagonals must agree with the rows.

How Many Cells Are Blank on Each Sheet?

Six when the square is built from 1 to 16, seven when its numbers grow as large as 100. A line is always complete at the start, and some line always lacks a single number, so the square can be finished one cell at a time.

Who Are These 4x4 Squares For?

Children who already enjoy the 3x3 squares and add two-digit numbers with ease, often from third grade, and adults who like number puzzles. The large cells make the sheets easy to read and to correct.