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The Four Fours Puzzle

December 28th, 2011 by Steven Pomeroy | 1 Comment | Filed in Math Games, Math Puzzles

The Four Fours

Here is an interesting math puzzle that you can play just about anywhere.  All you really need is paper and a writing instrument.  A calculator is not needed, but it is highly recommended!  The rules of this puzzle are simple enough, although there are some variants.  The rules given here are the ones I was given when I first learned of this math puzzle.

Using four fours, you are to find a mathematical expression for every whole number you can starting with zero.  You can use addition, subtraction, multiplication, division, factorials, decimal points, exponents, 0.4bar (i.e., the recurring decimal 0.44444. . .), and square roots.  Use of parentheses to emphasize the order of operations is not only allowed, but encouraged!

Some examples are:

0 = (4 + 4) – (4 + 4)

17 = (4 x 4) + (4 ÷ 4)

The Four Fours puzzle (a.k.a., The Four Fours Problem) has been known for years, and was described by Walter William Rouse Ball in his publication “Mathematical Recreations and Essays”:

four fours puzzle










Often times, there are multiple possible solutions.  How many can you find?

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