The most important trait for puzzling?

Question

I was wondering what the most important trait for a puzzle creator and/or solver was. I think I've found the answer, but I could be wrong. I thought about it, deconstructed it, put it back together a different way and took it apart again.

In the end, I'm fairly sure that trait is ____________... what, you thought I'd just tell you? No, I worked too hard to figure it out. You'll need to find it yourself. I wrote it down, but it might be hard to read:

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That's it, 12 tiles. But can you find the hidden trait written on them? It won't be easy. You'll know you've found it when you find a 12 letter word. Good luck!

Hint:

To sort one set, you'll need to sort the other.

Answer 1

Building on rand al'thor's and DooplissForce's answers:

Rearrange the tiles so the blue shapes match up:

This says "BLAISE", which implies Blaise de Vigenère, meaning we'll probably have to use the Vigenère cipher somewhere.

Rearrange the tiles so the red shapes match up:

Which spells DANGER. Perhaps the Vigenère key is DANGER?

Another observation:

Each of the twelve squares has one capital letter and one lowercase letter. That makes 12 capitals and 12 lower-case letters. I recorded the pairs of letters e.g. U and w, A and f. That gives us: UACOIWQSKGEM wfrexjakzgry

Given the clue "To sort one set, you have to sort the other":

Notice that the lower-case letters have two 'r's, but the capital have no repeats. That suggests that we should sort by the capitals. Once I started to sort the capitals, I notice that they are regularly spaced, 'A C E G I...', which indicates that I'm on the right path. The sorted letters are now: ACEGIKMOQSUW frrgxzyeakwj

Taking the lower-case letters:

Use 'DANGER' as a Vigenère key on them

Resulting in:

creativeness!

Answer 2

(Partial answer)

Adding onto rand al'thor's answer, I rearranged them so all the blue shapes matched up:

This says "BLAISE", which implies Blaise de Vigenère, meaning we'll probably have to use the Vigenère cipher somewhere.

Stealing from rand, the red shapes make:

Which spells DANGER. Perhaps the Vigenère key is DANGER?

Another observation:

Each of the twelve squares has one capital letter and one lowercase letter. Since there are thus twelve of each, and the code we're looking for has twelve letters, I don't think this is a coincidence. I tried using DANGER as a Vigenère key for the strings UACOIWQSKGEM, wfrexjakzgry, CWGIASUMQKEO, and rjgxfkwyazre, the strings gotten when you take the capital/lowercase letters going left to right, top to bottom, in each picture, and got:
UACOIWQSKGEM -> RAPIEFNSXAAV
wfrexjakzgry -> tfeytsxkmanh
CWGIASUMQKEO -> ZWTCWBRMDEAX
rjgxfkwyazre -> ojtrbttyntnn
i.e., nothing intelligible.

Answer 3

Partial answer

Rearrange the twelve squares so that all the red shapes match up:

They seem to spell out DANGER.

Then do the same for the blue shapes:

They seem to spell out BLAISE.

Note that the sentence in the OP "I thought about it, deconstructed it, put it back together a different way and took it apart again." is a hint telling us what to do here.

Sadly, rearranging these letters doesn't seem to give anything useful. Perhaps the twelve-letter word we seek is

DANGERBLAISE!