The Power of 4 Fours in Generating Whole Numbers

Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined: it is limitless as that space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer’s gaze.

J. Sylvester

Glad you came by. I wanted to let you know I appreciate your spending time here at the blog very much. I do appreciate your taking time out of your busy schedule to check out Math1089!

In mathematics, whole numbers are the part of the number system that includes all the positive integers starting from 0. In set theoretic notation, the set of whole numbers is W = {0, 1, 2, 3, 4, . . .}.

On other hand, among many mathematical operations, addition (+), subtraction (−), multiplication (×), division (÷), reciprocal (1/x), exponentiation (a^x), square root (√), concatenation (xx), factorial (!) etc. are well known. Of course, we should not forget fraction (a/b) and decimal (.).

There is a famous mathematics problem in which we are allowed to use only 4 fours and any mathematical operations to generate various whole numbers. In this article, we will show the way to generate whole numbers up to 20 using 4 fours. But we can generate other numbers also. Here, we have considered a few ways to represent a particular number, so the list is not exhaustive. If you came across any other way(s) to represent a number, not listed here, please do get back to us.

First we will generate the whole numbers 0, 1 and 2. The list is given below.

Next, we will generate 3, 4, 5 and 6. The list is given below.

Once done with numbers up to 6, now we will consider numbers 7, 8, 9 and 10. A list is given below.

Once done with numbers up to 10, now we will consider numbers 11, 12, 13 and 14. A list is given below.

Next, the turn for the numbers 15, 16 and 17. A list is given below.

Finally, the turn for the numbers 18, 19 and 20. A list is given below.

Of course, we can include other whole numbers in this list. A second blog containing the numbers from 21 to 50 will appear very soon as a continuation to this one.

Your suggestions are eagerly and respectfully welcome! See you soon with a new mathematics blog that you and I call “Math1089 – Mathematics for All!“.