To review, below is a puzzle from an IQ test for “geniuses.” The full question, explanation and its 8 multiple choice answers can be found in the original post.
@@% – &&@ – %&&
%&@ – @&% – %@@
%&& – %%@ – @&%
– – –
&@% – &@% – &@%
&@& – &%@ – @&&
%%@ – @&% – %@%
– – –
%&% – %@& – ???
@&@ – %&% – ???
&@% – &@@ – ???
– – –
Now, here’s how to solve it.
First, “solve” simply means to choose the correct answer out of the eight possible choices given. You do not have to “prove” the puzzle (we will get to that later for extra credit points) which would be to produce the correct answer without the aid of potential answer choices.
This distinction is very important because in “solving” a puzzle process of elimination (POE) is your best friend. What does that mean? It means the answer choices are just as useful as the puzzle itself.
With that said, let’s get to work!
Take a cursory glance at the puzzle. Anything jump out at you? Not really? Of course not, this is supposed to be hard! Ok, let’s think for a second. What we’re really trying to do is find some pattern that repeats itself throughout the 8 3×3 boxes. Realistically there are probably many patterns (again, this is supposed to be hard) but let’s start with trying to find just one.
What is a necessary characteristic of patterns? Repetition. Do you see any repetition of symbols or groups of symbols? I don’t. Okay there are a few patterns (two that I see) but not one that could solve the puzzle on its own.
Another common pattern type for these kinds of questions is rotation. For example, what appears in the bottom right corner moves to the bottom left, then upper left and so on. Are there any instances of rotation in the question above? Nope.
So we’ve spent about a minute on the question itself, looking for any obvious clues and have not found much of anything. No problem. Let’s look at the answer choices.
A. B. C. D.
%%@ %@@ %@@ &&@
&&% %&@ %&@ &@%
@@& &%& &&% @%%
E. F. G. H.
&%@ %@@ @@@ &%%
%@% %%@ %%% &&@
&&@ &&& &&& %@@
Do any of these choices seem clearly wrong? I certainly hope so. Consider “G”. There isn’t one instance of the same character repeating throughout one row or column anywhere in the puzzle above. Thus, it’s pretty unlikely each row in the answer would be made up of one character. Make sense?
More on the same point. Does it seem odd there are no cases of one character making up an entire row or column in the puzzle? Well, kind of.
Think about it: each box has 3 rows and 3 columns, making 6 chances for one character to make up a row or column. There are 8 boxes. 8×6=48, thus there are 48 chances in the entire puzzle for one character to make up an entire row or column. 3 characters for 3 spaces = 27 possible combinations, in 3 of which one character makes up an entire row/column, a 1:9 probability:
AAA BBB CCC
AAB BBA CCA
ABB BAA CAA
ABA BAB CAC
AAC BBC CCB
ACC BCC CBB
ACA BCB CBC
ABC BAC CAB
ACB BCA CBA
Thus, if the characters were arranged randomly there would be 5-6 instances on average in which one symbol would make up an entire row or column in the puzzle above. In our case there are 0. There’s 1.5% chance of that happening if the characters were indeed random. Aha!
The fact the chance of one characteristic of our puzzle (no rows or columns made up of only one character) occurring under normal circumstances is nearly 1:100 is not a coincidence or a chance happening. It’s a pattern, and we can eliminate any answer choices that do not comply with this pattern – G and F are gone.
Let’s take this a step further. What about one character repeated like @@& – two in a row so to speak? I’m not going to do the math again but suffice it to say in a random group this would be a VERY common occurrence. In our puzzle it only happens 12 times (from left to right, top to bottom) 2 in the 1st, 2 in the 2nd, 2 in the 3rd, 3 in the 4th, 1 in the 6th, and 2 in the 8th.
So we’re seeing a common theme emerge – the puzzle involves abnormally random patterns. If we assume the answer follows the same rules (which is a pretty safe assumption) it follows the answer will be equally “random.”
With that in mind let’s take another look at the remaining answer choices. A, C, D and H all look fairly unlikely too. A has 3 consecutive “two in a rows”, C has two L shaped connected two in a row patterns which don’t appear anywhere in the puzzle, H has the same thing and so does D plus a diagonal line of @’s. Given the extremely unusual (statistically speaking) lack of repetition and symmetry found in the puzzle it is very unlikely any of these answers are correct.
That leaves us with B and E. They are both sufficiently random but B has the same L pattern that was grounds for dismissing A, C, D and H (albeit they each have two L’s while B only has one), while E does not.
Thus, if you had to answer this question in a limited amount of time E would be the most reasonable choice. Why? Because there is a pattern throughout all 8 boxes in the puzzle and although we don’t have time to figure out exactly what that pattern is, we do know one of the characteristics of this pattern is a decidedly not random, “random” grouping of symbols. E is the answer choice that most closely mirrors this “random” grouping so that is – or at least appears to be – the most reasonable answer.
And guess what? It’s the right one too! That’s all for now, I’ll post a proof for the puzzle later this week.