That’s interesting! I got the same answer but I visualized it differently. (Imagine, for each possible subpattern, i.e. “plus shape” or “dots”, considering which items it appears in. In each case the answer is four, forming a rectangle. Two of the rectangles should extend into the ninth item, the one we’re looking for.)
This is a better answer than XOR, in a sense: it describes the pattern more narrowly. If the “true pattern” were XOR, it would be possible to have a shape or subpattern occur 6 times (if it is missing once from each row and column, e.g. if it is present everywhere except in one of the diagonals). Since this does not occur for any of the six shapes, this provides some evidence that XOR is not the “true pattern”.
(Similarly, this is very strong evidence that “just have 4 of each shape” is not the true pattern: there are 126 ways to place a shape in 4 cells, and only 9 of them make a rectangle shape. The case against XOR, where we notice that only 9 of the 15 XOR patterns are used, is much weaker, but I still believe it.)
Of course, if the goal is to just solve this particular problem, then any method works. But if we were studying the appearance of many matrices with this pattern, then you would get twice as many research points as anyone else :)
The relationship between this approach and the XOR approach is interesting, I think. Thinking in XOR terms requires fancier mental infrastructure—you need to have seen something like the idea of XOR before, and to be able to notice slightly subtle relationships between different parts of the figure. On the other hand, spotting that particular features tend to occur in rectangles involves spotting simpler things but paying more global attention to the whole figure.
It feels like these play to different aspects of cognitive ability; spotting complicated patterns versus spotting large ones, so to speak. I guess the latter is closely related to working memory size, which I know is generally thought to be a large contributor to measured IQ. The former seems like an important aspect of intelligence too, and strikes me as more likely to be trainable than working memory size.
I got the answer fairly quick (didn’t time it, but probably about a minute or two). In my head, I was thinking of subtraction, not even “cancelling out”.
In a row, cell 1 minus cell 2 equaled cell 3.
I suppose that is an XOR pattern after all, but you only need knowledge of basic arithmetic to verbalize the pattern.
(edit: upon rereading my answer, I guess it’s not fair to call it a subtraction only, since I’m still keeping around shapes from cell 1 or cell 2 provided they weren’t subtracted. Apparently my brain is doing XOR while thinking of it as a subtraction)
Yup, that’s about the level of fanciness. Not too bad, as you say, but I think harder to think of than four things forming a rectangle. (But maybe easier to notice, as I suggested above.)
I did it even more simply than that: Count things. Most have four iterations. Some have three iterations. The ones with three, make four. Less than 10 seconds for me. Same answer as the rest of everyone.
This is how I did it. My first instinct was to decompose the problem into the shapes {dots, circles, diamonds, square, +, X} and then plot which cells the shapes appear in. It’s pretty easy to see the rectangles after that. Though, I didn’t make the connection to XOR.
That’s also interesting… I think the two ways of looking at it are equivalent, i.e. any pattern that satisfies one should also satisfy the other. (Only because the XOR pattern works both vertically and horizontally.)
The way I solved the problem hasn’t been mentioned here by anyone, which is slightly bugging me out.
The way I solved it was looking at the whole puzzle as a single picture. The two bottom rows (except for the middle column) have pluses. Thus the solution must have a plus. The two right columns (except for the middle row—a transposed pattern from the previous pattern) have squares; the solution must have a square. There’s only two answers with both a square and a plus; I picked the one that seemed most intuitively correct.
Similarly, I go the same answer, but only by process of elimination. I knew it didn’t have dots, I knew it didn’t have a diamond, I knew it didn’t have an x, by just extrapolating from the “cut offs” in the problem. That left me with 2, but it felt...wrong. It didn’t feel intuitively right. If I had to pick on without thinking about it, number 2′s the last one I’d pick.
I only understand the pattern in a cohesive way from looking at the comments. Now it makes sense, instead of being deduced from bits of dis-unified information.
That’s interesting! I got the same answer but I visualized it differently. (Imagine, for each possible subpattern, i.e. “plus shape” or “dots”, considering which items it appears in. In each case the answer is four, forming a rectangle. Two of the rectangles should extend into the ninth item, the one we’re looking for.)
This is a better answer than XOR, in a sense: it describes the pattern more narrowly. If the “true pattern” were XOR, it would be possible to have a shape or subpattern occur 6 times (if it is missing once from each row and column, e.g. if it is present everywhere except in one of the diagonals). Since this does not occur for any of the six shapes, this provides some evidence that XOR is not the “true pattern”.
(Similarly, this is very strong evidence that “just have 4 of each shape” is not the true pattern: there are 126 ways to place a shape in 4 cells, and only 9 of them make a rectangle shape. The case against XOR, where we notice that only 9 of the 15 XOR patterns are used, is much weaker, but I still believe it.)
Of course, if the goal is to just solve this particular problem, then any method works. But if we were studying the appearance of many matrices with this pattern, then you would get twice as many research points as anyone else :)
The relationship between this approach and the XOR approach is interesting, I think. Thinking in XOR terms requires fancier mental infrastructure—you need to have seen something like the idea of XOR before, and to be able to notice slightly subtle relationships between different parts of the figure. On the other hand, spotting that particular features tend to occur in rectangles involves spotting simpler things but paying more global attention to the whole figure.
It feels like these play to different aspects of cognitive ability; spotting complicated patterns versus spotting large ones, so to speak. I guess the latter is closely related to working memory size, which I know is generally thought to be a large contributor to measured IQ. The former seems like an important aspect of intelligence too, and strikes me as more likely to be trainable than working memory size.
(I did it with XOR.)
I had the same reaction to calling it “fancy”.
I got the answer fairly quick (didn’t time it, but probably about a minute or two). In my head, I was thinking of subtraction, not even “cancelling out”.
In a row, cell 1 minus cell 2 equaled cell 3.
I suppose that is an XOR pattern after all, but you only need knowledge of basic arithmetic to verbalize the pattern.
(edit: upon rereading my answer, I guess it’s not fair to call it a subtraction only, since I’m still keeping around shapes from cell 1 or cell 2 provided they weren’t subtracted. Apparently my brain is doing XOR while thinking of it as a subtraction)
Yup, that’s about the level of fanciness. Not too bad, as you say, but I think harder to think of than four things forming a rectangle. (But maybe easier to notice, as I suggested above.)
I did it even more simply than that: Count things. Most have four iterations. Some have three iterations. The ones with three, make four. Less than 10 seconds for me. Same answer as the rest of everyone.
I did it this way too. I can’t help feeling like the xor way is smarter.
This is how I did it. My first instinct was to decompose the problem into the shapes {dots, circles, diamonds, square, +, X} and then plot which cells the shapes appear in. It’s pretty easy to see the rectangles after that. Though, I didn’t make the connection to XOR.
That’s also interesting… I think the two ways of looking at it are equivalent, i.e. any pattern that satisfies one should also satisfy the other. (Only because the XOR pattern works both vertically and horizontally.)
The way I solved the problem hasn’t been mentioned here by anyone, which is slightly bugging me out.
The way I solved it was looking at the whole puzzle as a single picture. The two bottom rows (except for the middle column) have pluses. Thus the solution must have a plus. The two right columns (except for the middle row—a transposed pattern from the previous pattern) have squares; the solution must have a square. There’s only two answers with both a square and a plus; I picked the one that seemed most intuitively correct.
Similarly, I go the same answer, but only by process of elimination. I knew it didn’t have dots, I knew it didn’t have a diamond, I knew it didn’t have an x, by just extrapolating from the “cut offs” in the problem. That left me with 2, but it felt...wrong. It didn’t feel intuitively right. If I had to pick on without thinking about it, number 2′s the last one I’d pick.
I only understand the pattern in a cohesive way from looking at the comments. Now it makes sense, instead of being deduced from bits of dis-unified information.
Do I know my IQ now?
I got the four, but not the rectangle—I just noticed that two elements only appeared three times.
Also how I did it. FWIW I know it took me more than a minute, but definitely less than five.