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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).
arccos(-4*4/4/4)
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Too funny. If you knew anything about the Numberphile channel, you'd know these are real mathematicians, not some BS. It's really just a math-related brain teaser. I really enjoy their videos. Even if you're not into math, they are sufficiently nerdy that I think many slashdotters would appreciate them. In fact a couple videos ago they had an interview with Ronald Rivest who was one of the inventors of RSA encryption. He's a down-to-earth, articulate person. He mentiones how he invented the MD5 hash which was later shown to be flawed.
Anyway, yes it turns out with just log, square root, and multiplication, you can assemble any whole number between 0 and infinity with just four fours. Fairly useless, but a neat puzzle.