Can you work out the trial of wits without asking for a hint?

POSSIBLE SPOILERS

Question

Is it possible to work out the first and third trials of wits (part of the Temple of Trials - see background for details) without resorting to trial-and-error, or the other method?

Hover for "other method":

`The other method is asking the Monitor Bird for a hint`

Especially for the third trial, where there are a number of symbols with lines joining them up... I spent a long time looking in my wizarding companion at the various signs available to each familiar. I even got to the point of drawing matrices of possible symbols and then working through the permutations that each familiar had signs for...

After nearly two hours of struggling, I eventually gave up and resorted to the other method, after which I was able to solve the puzzle in under a minute. But the solution seems completely random!

Is it possible to work this puzzle out? Is there a viable explanation for the solution, or is the other method actually the only method?

Background

Hover for details on location of this puzzle in the game:

`The Temple of Trials is situated North East of Summerlands South and you go there after freeing Rashaad's daughter, Esther, from brokenheartedness.`

There are three trials, of which one is the Trial of Wits.

The trial of wits is made up of three rooms. The second room is easy:

Hover for second room solution:

`The second room is simply a picture puzzle - move the blocks to the appropriate place on the underlying picture so it doesn't look like there are any blocks at all.`

The first room has a maximum of 24 possible unique combinations, so it can be worked out through brute force if necessary. However, as this is a trial of wits, I assume there must be a way to work out the puzzle without resorting to trial-and-error?

The third room has a maximum of 5,040 possible unique combinations and cannot therefore be worked out through a brute force method in reasonable time.

• If you have unlimited attempts, bruteforce. Commented Mar 23, 2013 at 0:27
• @kotekzot I've updated the question to include a section on brute-force attempts. Commented Mar 25, 2013 at 13:11