impossible puzzle?

December 12, 2005 12:57 PM

I played this IQ test online a few days ago here: http://www.iqtest.dk/main.swf and didn't do too badly. However, the last question (no. 39) seems completely impossible. I worked out by elimination which answer must be the right one but I still can't figure out why it's right. Are there any genuises out there who can put me out of my misery please?
posted by leibniz to sports, hobbies, & recreation (43 comments total)

Can you summarize the question for us, so we don't have to take the whole test to find out what it is?
posted by beautifulstuff at 1:01 PM on December 12, 2005

Yes, what beautifulstuff said. Flash sucks.
posted by voidcontext at 1:05 PM on December 12, 2005

posted by null terminated at 1:05 PM on December 12, 2005

Oh never mind. I see you can skip to the last question without taking all the previous ones. And it's a graphical question, so it can't be easily described in text.
posted by beautifulstuff at 1:06 PM on December 12, 2005

Here's a copy of the question:
posted by I Love Tacos at 1:08 PM on December 12, 2005

Tic tac toe boards?
posted by smackfu at 1:09 PM on December 12, 2005

null terminated: great minds think alike, but yours thinks about 3 minutes earlier.
posted by I Love Tacos at 1:09 PM on December 12, 2005

What's the correct answer? Is it C?
posted by j.edwards at 1:10 PM on December 12, 2005

nah, I got a 5 minute head start.
posted by null terminated at 1:10 PM on December 12, 2005

well, i can justify A, but it seems pretty weak. all the "ok" examples are "jumbled up", and the only way i can find to describe that compared to the candidates is by counting the size and number of straight "chains" of the same shape. there are no straight chains of length 3 and a maximum of 3 chains of length 2 (allowing for the same piece being in more than one chain). only "A" is consistent with that....
posted by andrew cooke at 1:26 PM on December 12, 2005

i guess if you count a chain of 3 as being two chains of length 2 that overlap you might simplify that rule. still seems unconvincing to me.
posted by andrew cooke at 1:28 PM on December 12, 2005

I think the answer is F, because the correct answer can't have a chain of 3 of the same symbols, where symbols can chain on sides but not corners.
posted by alms at 1:46 PM on December 12, 2005

Nevermind, I see the answer I gave is not correct. Time to keep thinking...
posted by alms at 1:46 PM on December 12, 2005

alms - a counterexample to that rule would be the lower center grid.
posted by mbd1mbd1 at 1:48 PM on December 12, 2005

oh, my answer isn't quite right because f would apply too. i suspect you could bend it slightly to give a bent chanin of 3 a lower weight...
posted by andrew cooke at 2:03 PM on December 12, 2005

this is hurting my head. why did you have to post this? argh.
posted by twiggy at 2:07 PM on December 12, 2005

the first one in the 2nd column is the 3rd one in the top row rotated 90 degrees to the left. same with the first in the 3rd row and the last in the 2nd row. jus' sayin'.
posted by soma lkzx at 2:07 PM on December 12, 2005

I think the answer is H, based on the pattern of duplicate shapes within each row.
posted by lester at 2:08 PM on December 12, 2005

I'm not sure the answer is visual. Might it be numerical? What if each square represented a specific number, and the sums for each symbol were somehow important? Am I making this too difficult?
posted by jdroth at 2:12 PM on December 12, 2005

OK; I have an idea. Each grid is a map of the overall layout. There is a square in each grid that corresponds to that grid's position in the overall layout (for example, the center square in the central grid, or the upper-right square in the upper-right grid). Let's call this square the grid's self-referrential (SR) square. Now, let's look for a pattern in the SR squares:

Left to right, from the top, we have:
X O T
O T X
O T ?

There are two patterns that I can see here. In horizontal rows, no SR square symbol is repeated. In vertical columns, exactly one SR square symbol is repeated exactly once. Both of these patterns can be completed by selecting an answer with an X in its SR square (the lower right). This leaves us with A,B,C,D, and F.

That's all I have now. As well as referring to themselves, however, the grids might also be referring to each other in this manner. I'm trying to work it from that angle.
posted by mr_roboto at 2:21 PM on December 12, 2005

Based on some rudimentary mathematical parsing (that probably makes sense only in my brain), I've pared my choices down to E, F, and H. (Seems like a lot of think F is a possibility.)
posted by jdroth at 2:22 PM on December 12, 2005

i suspect repeated cyclic permutations, but i'm still working on it...
posted by sergeant sandwich at 2:26 PM on December 12, 2005

The answer is C. I narrowed it down to C and F in a way that I can't explain in any Earth language, and F is like so obvious so it has to be C.
posted by TimeFactor at 2:28 PM on December 12, 2005

Actually, I take that back. It's F. In your Earth language: none of the original 8 has a group of like shapes that can all be navigated solely by non-diagonal moves. F is the only candidate for which that's also true.
posted by TimeFactor at 2:32 PM on December 12, 2005

Its odd. I've honed in on C and cant let go. Now I'm trying to work backwards to see what my brain seems to like about that choice.
posted by vacapinta at 2:33 PM on December 12, 2005

TimeFactor writes "In your Earth language: none of the original 8 has a group of like shapes that can all be navigated solely by non-diagonal moves."

The center grid in the bottom row has such a group of Xs.
posted by mr_roboto at 2:35 PM on December 12, 2005

OK, the answer's still F but not for the reason I gave (middle column, bottom row violates the rule I gave above). The reason: no corners of all one shape and all adjacent sides have all three shapes.
posted by TimeFactor at 2:37 PM on December 12, 2005

The answer is B and I will explain why:

In each row of boards each shape has one board where it occurs once in each column, and two in which it occurs twice in any given column.

In the first row of boards: in the first board Triangles occur once in each column, in the second board Xs occurs once in each column, in the third board Os occur once in each column.

In the second row of boards: first board is Xs, second board is Os, third board is Triangles.

In the third row of boards, first board is Os, second board is Triangles, third board is Xs.

I figured this out my second time through the test, and my score went up from 133 to 135 with all other answers left the same.
posted by Ryvar at 2:37 PM on December 12, 2005

I get B. Here is my reasoning:
Numbering the original patterns 1-2-3 in the top row, 4-5-6 in the second, and 7-8-9 in the third, we need to solve for #9. To get from 3 to 4, and 6 to 7, the patterns are rotated clockwise 90 degrees, as noted by soma lkzx above.
To get from 1 to 2, or 2 to 3, etc, shift all symbols to the right by one space (Anything shifted off the right end of the grid will move to the leftmost space in the next lower row. For the third row it will move the the leftmost space in the first row) At the same time change x's to o's, triangles to x's and o's to triangles.
The pattern matches in all cases and results in pattern B
posted by rocket88 at 2:47 PM on December 12, 2005 [1 favorite has favorites]

It seems Ryvar has "the" answer (based on the different scores) but but F still is "an" answer (modified from my last comment to eliminate D as well):
1) no corners of one shape.
2) no rows or columns of one shape.
3) adjacent rows and columns must have all three shapes
posted by TimeFactor at 2:47 PM on December 12, 2005

Ryvar: How does your schema exclude answer A?
posted by mr_roboto at 2:48 PM on December 12, 2005

OK, those criteria apply to C as well. I'm going back to my home planet. The answer is B.
posted by TimeFactor at 2:51 PM on December 12, 2005

I think rocket88 has it. Tricky.
posted by mr_roboto at 2:53 PM on December 12, 2005

rocket88: you say that to get from 1-2, shift all symbols 1 space to the right... that doesn't sem to apply for 1-2..

X A O
A O A
X X O

shifted right =

O X A
O A O
A X X

but 2 is:

A O X
A X A
X O O ...

Am I not understanding your logic?
posted by twiggy at 2:58 PM on December 12, 2005

Yes. rocket88 gives the right explanation for why B is the right answer. Very nice.
posted by TimeFactor at 2:58 PM on December 12, 2005

twiggy: from rocket88's explanation: At the same time change x's to o's, triangles to x's and o's to triangles.
posted by TimeFactor at 3:00 PM on December 12, 2005

good job rocket88, now tell me the meaning of life.
posted by JeNeSaisQuoi at 3:00 PM on December 12, 2005

I should have more fully explained my method, but it was, it turns out, wrong.

In my method I not only looked at the one shape which had one in each column of a given board, but made sure that both other shapes had two in an arbitrary column. This applies in all 8 'givens.' However, this rule does NOT hold true for D and F. Unfortunately, both A and B would be valid answers using my method.

The first time I went through the test I marked 'A' before I hadn't time to fully study the question. The second time I studied it, ignored 'A' because I'd used that answer last test, and therefore marked 'B' and noticed the higher score.

My bad, and rocket88 wins.
posted by Ryvar at 3:04 PM on December 12, 2005

twiggy -

You did the shift-right per what rocket88 said to do, but not substitution/change:

change x's to o's, triangles to x's and o's to triangles
posted by WestCoaster at 3:36 PM on December 12, 2005

I wonder if this question was lifted from this.
posted by Rhomboid at 3:41 PM on December 12, 2005

My girlfriend can't understand why I won't do sudoku puzzles. I've tried to explain to her that I've done Avogadro's number of logic puzzles in my life and there is nothing for me to prove by doing another one. She says I need to exercise my mind, apparently failing to notice that my daily reading lately has consisted primarily of invertebrate paleontology, developmental molecular genetics, and astrophysics, or that I'm building a system to bounce radio signals off the moon.
posted by neuron at 4:15 PM on December 12, 2005

You just had to know some smart fucker would be here to solve this. Kudos rocket88; that was a very complex pattern. Catching both the shifting and character changes was quite a trick.
posted by caddis at 6:06 PM on December 12, 2005

thankyou so much rocket88, your answer is beautiful.
posted by leibniz at 2:54 PM on December 13, 2005