This post contains the solution to a puzzle I recently saw on Google+ so in some sense it could be viewed as a 'Spoiler'.
However I'll NOT reference the puzzle itself so you must have solved the puzzle in a similar way to recognize it, or read the sample $\LaTeX$ below and recognize what it is talking about. And to be fair I did not just instantly recognize the first 11 terms of the Fibonacci Sequence as the answer to the puzzle but instead constructed the set backwards and only realized what it was when I got near the end of it, it was a major 'Ah-Ha' moment for me.
This post is about a really cool app that I just downloaded for my iPad Mini. The parent application, which I've had for a while, is called "MyScript Calculator For iOS" and is a 'finger writing' app that parses what you write into instructions for a calculator. So you write on the screen with your finger 1+1= and the app converts your finger writing to the graphic "1+1=2" and also as input into a calculator function thus not only figuring out what you wrote but additionally evaluating the expression, pretty cool. The app is free and a lot of fun to play with. The app is limited to simple algebraic and trigonometric functions.
However, inside the "MyScript Calculator" app you can access/download/in-app-purchase other apps, in particular "MyScript MathPad". Again you do finger writing and it converts it to a mathematical expression in graphical form, but no calculator option is invoked (I suppose it it did that automatically then it would be a really fine mash-up with Sage or Mathematica).
You get a choice of saving the result as a graphic, or as $\LaTeX$ code or as a MathML script. To save in either as $\LaTeX$ code or in a MathML script you have to opt for the paid version of the app (US4.99). The parent company of the app is: VisionObjects.COM.
The app "MyScript MathPad" is a huge part of the guts of a project I came up with some years ago: HenScratch.org. This only goes to show if you wait long enough all your ideas will turn into just a bunch of mash-ups of stuff other folks figure out for you.
Below is some $\LaTeX$ code I wrote with my finger then exported from the app (the puzzle solution) and copied into this blog post. When I exported it (which was when I found out I had to pay US4.99 to 'unlock' saving it to $\LaTeX$ code) and then copied the $\LaTeX$ code into this post.
Note: To get $\LaTeX$ code to display in a blogspot.com blog you have to modify the template of your BlogSpot blog to have a couple of MathJax scripts to the template (edit template header html source) and then enclose the code in some special characters, I use single and double 'dollar-signs' for in-line and multi-line code.
Note: Also I edited the $\LaTeX$ code to have the words 'if' and 'then' and 'such that' since the finger writing app does not allow text to be easily inserted.
if
$\quad S=\left\{ 1,1,2,3,5,8,13,21 \right\}$ then $\nexists x_{ 1 },x_{ 2 },x_{ 3 } \in S$ such that $x_{ 1 }+x_{ 2 }>x_{ 3 }$
