Sunday, November 4, 2012

What is going on here?

Spoiler warning: This post contains a picture of one of the Raven's matrices from the IQ test suggested in the Less Wrong reader survey.

There's rather a nice little IQ test app here:  (If you want to go and take it, do so before you look at the picture below!)

I scored 130 on it, which makes me think that the leetle grey cells may be falling apart under the influence of alcohol and old age. In youth, I usually got between 150 and 160 on these things (they're not terribly accurate near the ends of their scales).

Anyway, my powers are obviously declining. What's worse is that even when not under time pressure, I can't figure out what the answers to the questions are. Can anyone figure out which of the eight possible choices here completes the figure? And explain why? It's completely opaque to me.

If anyone has a go at this, the questions I can't do are 26, 29, 33, 34, 35, 36, 37, 38, 39. And I'd be really grateful for an explanation of what any of those are about.

Aha! gives an explanation of how these things work. After reading it I went back and can now complete the test in about 10 minutes (which gives me a score of 145+, apparently that's as good as you can do.). Most of the answers are indeed obvious in retrospect, although there are a couple where I can't decide between two choices, and one where I'm a little sceptical I could have worked out the pattern having never seen it before.

The particular one above works by adding the dots. dots outside the figure cancel with dots inside. As far as I can see, the dot positions are irrelevant and random. In terms of crossword clues, this would be OK in the Telegraph but not meet the standard for the Times.

In fact, I've now got some thoughts about the analogy between IQ tests and cryptic crosswords. They seem closely related in terms of what they're measuring, although obviously these visual patterns are language neutral, whereas I can't see how you could hope to do a cryptic in English unless you were a native-standard speaker. I might try to work this up into a blog post later.


  1. FWIW, (1) my score was just slightly over 130 and I'm pretty sure I'm 150 or so by any reasonable measure, and (2) I was baffled by that particular one as well. (I haven't looked at it without the time pressure, beyond about a minute right now in case anything jumped out at me, which of course it didn't; perhaps all would become clear with slightly longer consideration. But I doubt it.)

    Since your readership overlaps at least a bit with that of LW, you might want a spoiler warning at the start.

    1. thanks g, added spoiler warning.

      Quite a lot of the later questions seemed senseless even if you 've got a while to think about them. Can you explain any of the last six?

    2. I'm pretty sure I got a few of those. I'll take a look after I get home (long day at work today).

    3. 26: lines from W, centre, E dots rotate clockwise, each step being 45 degrees if possible but 180 degrees at the edges.

      29: take shape from L column, replace its edges with what's in middle column, get R column. Note the orientation of the middle column to distinguish A from E.

      33: each NW-SE broken diagonal consists of two wavy lines and their union.

      34: what the fuckety fucking fuck?

      35: reflect arrows on left in mirrors in middle to get arrows on right.

      36: sorry, my brain exploded.

      37: we're working TL to BR in reading order. The progression of black squares is obvious. One filled circle begins at (1,1) and moves right one space each time, moving down to the start of the next line when it reaches the end. Another does the same starting at (3,1). An empty circle starts at (1,1) and does something I haven't quite worked out. The black squares are in front, then the empty circles, and the filled circles at the back. This is enough to determine the answer. (I *think*. One horrible possibility is that actually there are two empty circles and the "z-order" changes in some funny fashion, in which case one other answer might be just barely possible.)

      38: moving L->R and T->B, apply a stretching operation for a single-headed arrow and a colour interchange for a double-headed arrow.

      39: OMG. Perhaps there's something like ternary arithmetic going on here, but I wasn't able to figure it out in the time available. I'm not going to try now because it's well past bedtime.

      Hope this helps.

    4. Actually, now I think of it, I think I did come up with a kinda-sorta answer to 36, which I didn't really believe very much. The idea was that there ought to be three each of {black, length 1}, {black, length 2}, ..., {light grey, length 3}, which determines the distribution of lengths in the BR space and leaves only two options; I forget what halfassed justification I had for preferring one over the other.

    5. g, nice answer for 26. The cheat site has 'rotational symmetry plus all middle dots covered', which leaves the answer ambiguous. I like your answer very much and am fairly confident that I wouldn't have seen that myself.

    6. I'm fairly sure that 34 is addition, with internal balls cancelling external balls, and the orientations are just a herring. There seems something evil about a puzzle where there are things you have to ignore.

    7. I (eventually) came to the same conclusion about 36. I think the disambiguation is is the base of the bar chart (left, right, bottom) in the usual broken-diagonal pattern.

    8. 37 I think is two circles moving in reading order as the chessboard fills, but if they get hidden by squares they change colour.

    9. 38 looks like composition of operators, if you take one head to mean stretch, two heads to mean colour swap, and cross to mean rotate. Then the whole grid works nicely.

    10. 39 is: As you go along a row, shuffle symbols down in reading order, while permuting (cross circle triangle).

    11. Yeah, I looked at the cheat sites eventually too :-).

  2. Replies
    1. Wow, you strike me as being a bit more than top 20% for cunning.

    2. William, is there a question you can't do that I can (listed the ones I can't do above)? Or do you have the same experience as me that most are obvious and some seem to have no pattern?

  3. I think I agree with your list (I also couldn't do 31 at the time, but can now). I may have guessed a couple off your list, which may have counted against me if I guessed wrong.

    Miriam can't do 34 either, and she's better than me :-)

  4. Ah, and 26 (in retrospect) is presumably G - the second set of lines have rotated, and are now outside the visible square.

    I think 29 is E, but I find that only weakly convincing.