Math Puzzles designed to grow your mind


Math puzzles come in many styles, including: numbers, arithmetic, algebra

and combinations (Sudoku, Kakuro, Coded, Towers of Hanoi, Magic Square ).

Below we will explore some of the more common math puzzles ( this list is not meant to

be all-inclusive) , most of all we hope you will enjoy the selections.


Numbers, Arithmetic, and Algebra

  • Cross-figures or Cross number Puzzle

Like crossword puzzles in structure, only numbers are used instead of letters.

Clues may appear in the form of historic dates( Year of Columbus' voyage to America ),

math equations ( 15 times 25), one answer may relate to another ( 3 times 4-down),

or even embedded in another clue ( 7-down reads :"see 13-across" :reads " 7-down

plus 5"). Most puzzle enthusiasts agree the more challenging puzzles have no-clues at all.

Another common theme to these types of puzzles is that zero is often not used ( grids

typically restricted to the numbers 1-9).

We have working examples on our page entitled computations (click here to visit)

  • Four fours

Is an interesting mathematical puzzle because the goal of the game is to use the simplest

mathematical operators( -, +, *, / ) for every whole number say from 0 to some arbitrary

maximum, and the digit four. Most versions require using only four expressions as well.

What I find to be most exciting about this math puzzle game is that the solutions can be varied

and creative. For example here are some possible solutions to yield the results for 0,1, 2

using only fours, with four expressions( here we are using four as an integer) .

0 = (4 / 4) x 4 - 4 = 0

1 = (4/4) + 4 - 4 = 1

2 = 4 - (4 + 4) / 4 = 2

Can you think of any alternatives or solve for 3, 4, or 5? ( See solutions section at the

bottom of this page).

  • Word Arithmetic

These are problems where you are given certain facts in a paragraph and must

decipher the answer through a series of mathematical iterations.

As an example :

Suppose a 4-digit number is an exact multiple of 9, and three of the four digits

are 1, 2, 3. What is the fourth digit? (See solution below)

Want more Word arithmetic problems? Click here

  • Verbal Arithmetic

Also known as alphametics, crypt-arithmetic, cryptarithm or word addition,

is a type of mathematical game consisting of an equation among unknown

numbers, whose digits are represented by letters. The goal is to identify the

value of each letter. The name can be extended to puzzles that use non-alphabetic

symbols instead of letters. The equation is typically a basic operation of arithmetic,

such as addition, multiplication, or division. Below is a classic example:

Traditionally you can solve with the digits 0-9. (See solution below).

To play these types of verbal math puzzles ( with help and hints click here for

our Verbal Math games section).

  • Magic Square

Traditionally, the magic square consists of a board of say 16 squares with 15 numbered spaces

and one empty space , you have to order (arrange) the numbers from 1-15 , by sliding them along

the grid, you can play now :

Play Magic Square Game!


  • Choose a Level (3 to 10).
  • The game board consists of blocks with numbers in each block. Also there is an empty space that can be used for moving the blocks.
  • The objective of the game is to order the numbers using the empty space for temporary movement.
  • Press the "Start Game" button. The timer will start.
  • Move blocks in a row by clicking on them. A block can be moved only if it is in the same row or column as the empty space.
  • You can move multiple blocks (in the same row or column as the empty space) by clicking the farthest block that you need to be moved.
Order all the numbers in the shortest time possible with a minimum number of moves...

Choose Level:



We have an excellent section regarding the Sudoku math puzzle (simply click on the

title above).

Similar to Sudoku, but not as popular, Cross Sums, (or Kakuro) puzzles are actually

mathematical transliterations of crossword puzzles, meaning we use numbers instead

of letters, click the title above to play.

Click above which directly links to our page for solving the Towers of Hanoi, using

mathematical procedures.


Four-Fours: 3, 4, 5.

3 = ( 4 x 4 - 4) / 4 . 4 = 4 + (4 x (4 - 4)) . 5 = ( 4 x 4 + 4) / 4 .

Solution Verbal arithmetic example

The solution to this puzzle is O = 0, M = 1, Y = 2, E = 5, N = 6, D = 7, R = 8, and S = 9.

What is the fourth digit?

If the number is an exact multiple of 9, the sum of it's digits must also equal 9, therefore

1 + 2 + 3 + x = 9, or x = 3.


MATHEMATICAL ASSOCIATION OF AMERICA (MAA): A professional society that focuses

on mathematics .

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