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HDD Killers

A Problem Of Squares

Posted on Monday 8 May 2006

I thought that perhaps y’all might like a bit of a brain teaser. I don’t know how many more of these little teasers there will be, or if there will be any more at all, but I created a category specially for them, I know, I’m a risk taker.

What is the first square number that contains one and only ONE zero?

In case you were wondering, no, this isn’t a trick question. The reason I write one in capital letters is because I want to stress that the answer is not 100, because that has TWO zero’s.

This one isn’t too hard, and I’m sure that most people reading this (yes, all both of you) would be capable of writing a little program to work it out for you. However, try figuring it out yourself first, using a calculator is fine but don’t just go through the numbers squaring them until you find a zero.

If you find the answer without too much bother or if someone has already posted the answer in a comment and you accidentally read it, try finding the next, and the one after that.

    Monday 8th May 2006 | 9:24 pm
    Stephen Philbin's Globally Recognised Avatar

    Errrrr. 0?

    Monday 8th May 2006 | 10:15 pm
    David's Globally Recognised Avatar

    OK, besides that one.

    Monday 8th May 2006 | 11:35 pm
    Neal V.'s Globally Recognised Avatar

    1024 perhaps?

    Tuesday 9th May 2006 | 1:08 am
    David's Globally Recognised Avatar

    Yep, that’s the one, any takers as to what the next one is?

    Wednesday 10th May 2006 | 4:07 am
    Stephen Philbin's Globally Recognised Avatar

    Errrrr. -1024?

    Wednesday 10th May 2006 | 4:18 am
    David's Globally Recognised Avatar

    -1024 is what you get when you multiply 32i by itself, but since 32i is an imaginary number, that doesn’t count.

    From now on the definition of a square number (at least in this blog entry) is defined as the product of a natural number multiplied by itself. For those wondering, the natural numbers are just the counting numbers; 1, 2, 3 etc. Note that this set does not include 0.

    Wednesday 10th May 2006 | 4:33 am
    Stephen Philbin's Globally Recognised Avatar

    Ya big cheater.

    Wednesday 10th May 2006 | 4:38 am
    David's Globally Recognised Avatar

    Yeah I know, how DARE I use actual maths and properly define what exactly a square number is.

    Wednesday 10th May 2006 | 4:41 am
    Stephen Philbin's Globally Recognised Avatar

    Changing the rules afterwards. “Only natural numbers are allowed now”. 😛

    Wednesday 10th May 2006 | 6:04 am
    David's Globally Recognised Avatar

    Well, it’s kind of dubious as to whether 0 is allowed or not, some define a square number to be an integer multiplied by itself, others say it’s a natural number multiplied by itself.

    I chose the second definition since it makes more sense when demonstrated geometrically, also I knew it’d piss you off. 😛

    Wednesday 10th May 2006 | 6:34 am
    Stephen Philbin's Globally Recognised Avatar

    What’s so geometrically nonsensical about zero height by zero width having zero surface area!? It should be the first rule of geometry (it is after a pretty basic principle in life), that something is either there, or it isn’t.

    Wednesday 10th May 2006 | 1:08 pm
    David's Globally Recognised Avatar

    You answered your own question, if you have a square that has 0 height by 0 width, you don’t have a square, because you don’t have anything.

    Wednesday 10th May 2006 | 1:54 pm
    Stephen Philbin's Globally Recognised Avatar

    Yeah! Nothing is nothing! There has to be some nothing to allow the something to work properly.Imagine if there wasn’t any nothing in the universe. It’d all be completely full of somethings and we’d all be squished!

    Saturday 19th August 2006 | 7:35 pm
    Zach Blume's Globally Recognised Avatar


    Produced using this code:

    What do I win? :-p

    Monday 21st August 2006 | 7:52 pm
    David's Globally Recognised Avatar

    You cheated, so you win a trip to the dungeon.

    Monday 21st August 2006 | 8:12 pm
    Zach Blume's Globally Recognised Avatar

    I didn’t cheat, I used my resources. Screw calculators :-p

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