# Aptitude Assessment

I wake up with a dull headache, in a cramped and sparsely furnished room. I quickly realize that I don't know where, or even when, I am.

Still a bit groggy, I lean forward in the chair to try the door, only to realize that there's no doorknob.

Suddenly, a computer terminal behind me emits a soft chirp. Turning around, I notice an email has just arrived:

From: Globe Industries HR <globe-hr@globe.intranet>
To: PSE45720 <empl-pse45720@globe.intranet>
Subj: Aptitude Assessment

Hello, employee! Welcome!

We hope you find your new accomodations to your liking. At Globe Industries we believe that personal comfort is a factor that affects employee performance.

To get you warmed up, we have a mandatory puzzle for you.

Please take a moment to enjoy this passage from William Shakespeare's Macbeth:

As you were reading that, you may have noticed that the words are highlighted in various colors. These colors are not just random, they have meaning. Using this information, determine how the words Macbeth and Shakespeare should be colored.

We look forward to your future!

Globe Industries HR

This is an automated email. Attempts to reply will be penalized.

How strange, I think to myself, I've never even heard of a 'Globe Industries'. However, it looks like I've got no choice but to do as they ask. Better get started...

See and try the html here: https://jsfiddle.net/zrr81Ly3/. Thanks to GentlePurpleRain for doing the initial color conversion to a more unambiguous palette!

The full color list is: $$\begin{matrix} \text{Black} & \bbox[#000000]{\;\color{white}{\mathtt{\#000000}\;}} \\ \text{Orange} & \bbox[#e69f00]{\mathtt{\;\#e69f00\;}} \\ \text{Sky} & \bbox[#56b4e9]{\mathtt{\;\#56b4e9\;}} \\ \text{Green} & \bbox[#009e73]{\mathtt{\;\#009e73\;}} \\ \text{Yellow} & \bbox[#f0e442]{\mathtt{\;\#f0e442\;}} \\ \text{Blue} & \bbox[#0072b2]{\mathtt{\;\color{white}{\#0072b2}\;}} \\ \text{Red} & \bbox[#d55e00]{\mathtt{\;\#d55e00\;}} \\ \text{Purple} & \bbox[#cc79a7]{\mathtt{\;\#cc79a7\;}} \\ \text{White} & \bbox[#ffffff,border:1px solid black]{\mathtt{\;\#ffffff\;}} \\ \end{matrix}$$

These color names aren't exact (e.g. the one called 'red' is actually more of a vermillion), but my goal is just to give us a consistent name for each color to alleviate any ambiguity.

# Hints

1. The actual colors aren't important, only their categorization. Some of you may find using the list in the addendum below easier, treating the puzzle like a What is a Word™? puzzle with more categories.

2. There's a reason I use the <code> tags in the html, and put backticks around the text in the addendum. This reason is not that the text is monospaced.

This is a list of words from the text above associated with each color. Note that - is an instance separator, and words are taken from the text as-is, including punctuation when it's highlighted together with the word. So the last word from the text (in orange) is to be considered "nothing.", with the period included.

• Black: this - syllable - time, - candle! - walking - fury,
• Orange: yesterdays - Life’s - struts - idiot, - nothing.
• Sky: hereafter; - To-morrow, - to-morrow, - to-morrow,
• Green: Signifying
• Yellow: a - a - a - a - a
• Blue: been - and - and- pace - day - to - day - To - of - And - to - poor - and - stage - And - no - by - an - of - and
• Red: She - have - died - have - for - the - all - our - have - The - way - but - upon - the - heard - tale - Told
• Purple: There - would - word. - Creeps - in - petty - from - last - recorded - fools - death. - Out, - out, - player - That - hour - then - is - it - is - sound
• White: should - time - such - lighted - dusty - brief - shadow, - frets - his - more: - full
• I'm colorblind - anyone mind making a list of which words map to which colors? – Deusovi Nov 16 '16 at 5:04
• Sorry, @Deusovi and others, I should have thought of that. (Thanks for doing it, Alenanno). – Phlarx Nov 16 '16 at 15:44
• @Deusovi I tried my hand at creating a copy of the above using a colour palette that is supposed to be colour-blind-friendly. Can you let me know if it works for you? – GentlePurpleRain Nov 17 '16 at 19:17
• @Phlarx If you're interested in updating your colour palette, the names of the colours I used are here. – GentlePurpleRain Nov 17 '16 at 19:17
• @GentlePurpleRain thanks for finding that! I'll update my palette with that schema shortly. – Phlarx Nov 17 '16 at 21:25

Okay, this took me a while, but I've got it now.

Shakespeare is

Black

And Macbeth is

White

Reasoning behind this:

Words (or rather groups of characters, since punctuation marks count as well) are divided into groups based on the number of certain characters they contain.
Individual characters are scored as follows: 1 point for each "piece" they consist of, -1 point for each closed loop they contain.
c,f,h,k,l,m,n,r,s,t,u,v,w,x,y,z all score 1 point, since they're made up of only one piece and contain no cycles.
a,b,d,e,o,p,q score 0 points, since they're made up of one piece but also contain one cycle.
i,j score 2 points, since they're made up of two pieces.
g scores -1, since it's made up of one piece and contains two cycles.
The same reasoning applies to the punctuation marks and capital letters, but you get the picture.

For the groups this means:

Characters of words in the same group sum up to the same total:
Yellow words sum up to 0
Blue words sum up to 1
Red words sum up to 2
Purple words sum up to 3
White words sum up to 4
Black words sum up to 5
Orange words sum up to 6
Sky words sum up to 7
Green words sum up to 9
Since Shakespeare = 1+1+0+1+0+1+0+0+0+1+0=5, Shakespeare should be colored black and Macbeth = 1+0+1+0+0+1+1=4, so Macbeth should be colored white.

Fun fact:

Of all colors used only the word purple would actually keep its identity when being colored according to this scheme.

Thanks Phlarx!

• Ok, I was being dense. For future readers: font matters. – ffao Nov 22 '16 at 23:09
• Thanks for the edit, Rubio. I didn't realise the 'g' was different (1 vs. 2 cycles) – Levieux Nov 23 '16 at 7:51
• You got it exactly! Good job! – Phlarx Nov 26 '16 at 19:15

Just observations so far:

Did some analysis of which color groups' words contain which letters, sorted according to the number of letters missing:

Yellow: A (missing BCDEFGHIJKLMNOPQRSTUVWXYZ)
Green: FG I N S Y (missing ABCDEHJKLMOPQRTUVWXZ)
Sky: A EF H M O R T W (missing BCDGIJKLNPQSUVXYZ)
Blue: ABCDEFG NOP RST Y (missing HIJKLMQUVWXZ)
Orange: A DEFGHI L NO RSTU Y (missing BCJKMPQVWXZ)
Red: AB DEF HI L NO RSTU W Y (missing CGJKMPQVXZ)
White: AB DEFGHI LM O RSTU W Y (missing CJKNPQVXZ)
Black: ABCDEFG I KLMN RSTU W Y (missing HJOPQVXZ)
Purple: A CDEF HI LMNOP RSTU W Y (missing BGJKQVXZ)

Thought this had a slight chance of proving useful. I also observed from the above that

Assuming the missing letters are "forbidden" for each group (maybe not true but makes an interesting thought experiment), none of the groups contains the right combination of letters to make Shakespeare (at least one of its letters are missing in every group), and only the black color group has the right letters to make Macbeth.

No definitive answer yet, just some observations:

Summing word lengths per color and dividing by number of words for each color we get:

$\small\begin{array}{rcc}\textbf{Color}&\textbf{SUM}&\textbf{AVG}\\\text{Black:}&33&5.50\\\text{Orange:}&33&6.25\\\text{Sky:}&33&8.25\\\text{Green:}&10&10.00\ \ \\\text{Yellow:}&\phantom{1}5&1.00\\\text{Blue:}&57&2.85\\\text{Red:}&60&3.53\\\text{Purple:}&88&4.19\\\text{White:}&53&4.82\end{array}$

Or, alternatively, counting only unique words:

$\small\begin{array}{rcc}\textbf{Color}&\textbf{SUM}&\textbf{AVG}\\\text{Black:}&33&5.50\\\text{Orange:}&33&6.25\\\text{Sky:}&17&8.25\\\text{Green:}&10&10.00\ \ \\\text{Yellow:}&\phantom{1}1&1.00\\\text{Blue:}&33&3.00\\\text{Red:}&46&3.54\\\text{Purple:}&83&4.37\\\text{White:}&53&4.82\end{array}$

Some notable things:

First of all, there's lots of 33's, which may, however, just be a coincidence.
Secondly, starting from Yellow the list is in ascending order for average word length.
Unfortunately the lists aren't fully disjoint: some Blue words are longer than some Purple words for instance.
There should be some meaning to this, though, so for now I would be guessing that Shakespeare would probably be Green and Macbeth either Black or Orange...

• This is a good observation! You're headed the right way :) – Phlarx Nov 16 '16 at 15:49

So here we go!

For Shakespeare

Pink

and for Macbeth

Lime (or whichever color was chosen for that first "hereafter". I'm very bad with colors)

Reason being,

I read the passage aloud - as apparently all Shakespeare must be - and it seemed words with the same color, had the same feel on delivery. So, I announced the play as I've heard before, and chose the colors where the words felt the same.

• Nice try! However, it's not the pronunciation, nor is this any special property of Shakespeare's works. (Also, wow, the colors look way different on this screen... I may have to tweak them a bit...) – Phlarx Nov 16 '16 at 2:48
• How can you just say that words "had the same feel"? That tells me nothing. – greenturtle3141 Nov 16 '16 at 3:50
• When I have to read Shakespeare, I need to walk around or none of it makes any sense at all. So when I was reading, the words seemed to me that they had similar stress, flow and movements attached to them. I don't know if that makes sense to anyone but myself, but that's what I thought. – J Sant Nov 16 '16 at 4:35