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

Posted by msmash on from the math-is-amazing dept.

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).

7 of 309 comments (clear)

  1. BS detector went off and is overheating by frovingslosh · · Score: 1, Insightful

    Any number? I'm pretty sure that you can't make pi with four 4's. Looks like the much lamer "any whole number", although I find even that pretty hard to believe.

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    I'm an American. I love this country and the freedoms that we used to have.
    1. Re:BS detector went off and is overheating by jeek · · Score: 5, Insightful

      arccos(-4*4/4/4)

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    2. Re:BS detector went off and is overheating by caseih · · Score: 5, Insightful

      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.

    3. Re:BS detector went off and is overheating by frovingslosh · · Score: 1, Insightful

      That's kind of a circular argument. I guess you could also claim: 4+4-4-4+pi , claiming that that thing on the end is just a mathematical symbol and therefor a legitimate part of the equation.

      --
      I'm an American. I love this country and the freedoms that we used to have.
    4. Re:BS detector went off and is overheating by Nemyst · · Score: 4, Insightful

      You seem to be confusing operators (or, more generally, functions) with constants here. arccos is just an operator, much like negation, addition, subtraction, etc. Pi is a constant, a numerical value, it has no other interpretation.

  2. Re:Um, no. by sexconker · · Score: 3, Insightful

    Yup. They say "normal math symbols" and then include concatenation. Fucking horse shit.

  3. Re:Um, no. by vux984 · · Score: 4, Insightful

    But not suitable for Slashdot where we (should) already know this stuff, there is nothing new here.

    Give it a rest.

    It was really an elegant mathematical solution.

    Yes its not new, but its certainly 'esoteric enough'; I certainly hadn't seen it before. I can understand the expression on the wikipedia article, but its definitely not something i'd think most people would follow; and even i would have had to study it longer than it the 5 minutes it took to watch the video to have figured out how it all worked, so I enjoyed seeing the derivation.

    And if some youtuber makes a few pennies off demonstrating an elegant mathematical proof in an easy to follow and informative way... what exactly do you object to about it?