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.

Errrrr. 0?

OK, besides that one.

1024 perhaps?

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

Errrrr. -1024?

-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.

Ya big cheater.

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

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

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. 😛

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.

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.

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!

1024

1089

2025

2209

2304

2401

2601

2704

2809

3025

4096

5041

6084

7056

9025

9409

9604

9801

Produced using this code: http://www.emptysnow.com/squares.php

What do I win? :-p

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

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