You Can Make Any Number Out of Four 4s Because Math Is Amazing (youtube.com)

Andrew Moseman, writing for Popular Mechanics: Here's a fun math puzzle to brighten your day. Say you've got four 4s -- 4, 4, 4, 4 -- and you're allowed to place any normal math symbols around them. How many different numbers can you make? According to the fantastic YouTube channel Numberphile, you can make all of them. Really. You just have to have some fun and get creative. When you first start out, the problem seems pretty simple. So, for example, 4 - 4 + 4 - 4 = 0. To make 1, you can do 4 / 4 + 4 - 4. In fact, you can make all the numbers up to about 20 using only the basic arithmetic operations of addition, subtraction, multiplication, and division. But soon that's not enough. To start reaching bigger numbers, the video explains, you must pull in more sophisticated operations like square roots, exponents, factorials (4!, or 4 x 3 x 2 x 1), and concatenation (basically, turning 4 and 4 into 44).

Comments

Um, no.

[rickb928]

"and concatenation"
No, that's not really maths,

But this is existing decomposition....

[aaronb1138]

This is essentially a 2^n + 0 or 1 formula which describes all natural numbers. Using 4 as a placeholder (2^2) is just lame, but the character of operations is the same.