Saturday, November 15, 2008

Gladwell's Outliers

I am not much of a book reader but I like a good book when I see one and will mostly end up buying it... Amazon must have become rich of the number of books I've been buying from them the last 10 years... and I never got a descent discount or extra bonus, damn them... Anyways, I also never managed to read a book thru more than, say, 10%, and for quite a few among them I've never even gotten thru the preface part... never mind.

Not this one. I knew Gladwell from Blink and The Tipping Point, both of which I own in print and audio format. Even so, I don't believe I ever managed to read any of those two in full but, in any case, I remember I was quite enthusiastic about the bits I eventually got thru. So, during wait time for my flight to Barcelona from the Brussels National last Thursday I fell upon Gladwell's latest, titled 'Outliers'.

I eventually surpassed myself by managing to swallow the 299 pages of the book in almost one go. By the time I have been landing back to Brussels from Barcelona yesterday at almost past midnight, I had been thru 3 quarters of the book which I eventually finished this morning. Almost never happened before. It must have been a real good book.

Above all, like his other two bestsellers, this is not a fiction book. It's not scientific either but as I know Gladwell, he does some hard research work before approaching a subject and to an agnostic it might seem kinda of 'scientific'... in any case the subject is fascinating and I found that I agreed wholeheartedly with most of what he writes. I often thought about these facts as well but I had no basis to explain the reasons behind them other than some 'theories' of my own... sort-of empirical kinda thing.

In a few words, Gladwell searches the reasons behind successful people (whom he calls outliers) and tries to break the myth that only the very smart succeed (those with highest IQ's so to say). His thesis is that you need to be at least of a certain smartness level but once you are there by birth, then it is a series of other factors that kick in... and he goes on about 'proving' his 'theory' about such factors by exposing a myriad examples and psycho-socio-research outcomes about individual success. The most fascinating part of the book I found to be the story about many Jewish immigrants, tailors and garment craftsmen from Eastern Europe, who arrived at the Bronx, NYC, at the end of the 19th and beginning of the 20th century to work themselves thru poverty and persistent hard labor and become successful entrepreneurs with the generation of their siblings becoming even better businessmen and the following generation turning into successful doctors, financiers and lawyers.

In his chapter about IQ and how being (IQ) smart could help someone get successful (but never that alone), he presents Raven's last IQ test question that I found quite interesting. I spent about half hour to figure it out before falling asleep in a dry Novotel room at Sant Cougat del Valles, west of Barcelona. I think I got it... Take a try by clicking on the scan above for sharper view and tell me why you think that is if I told you that A is the solution. I promised my youngest sibling a 100 euro bill if he found out... He's still trying... Let me pass a hint... the reason, I think, doesn't lie behind any patterns but behind appearance frequencies of the three card signs (hearts, diamonds and clovers*)...

Another intriguing chapter was developed about the reasons behind airplane crashes. Funny thing is, I started reading that part of the book by the time our plane was taking off at the Barcelona airport... And I am not too much fond of hanging 10 km above the ground at 900 km/hr. Even after I have flown thousands of hours in my life.

Anyways, that was indeed an extremely interesting book worth spending a few leisure hours to read. Another slam dunk for Gladwell getting a new National bestseller.

*I'll describe my solution in the 'reactions' below in a few days... I'd ruin the fun if I did it right away, nooot?


VJK said...

Ok, here's the solution... I think.

There are 9 squares with each one subdivided in 3 rows and 3 columns. Each intersection of a row with a column is a cell.

Each sign (H for hearts, D for diamonds and C for clovers) appears 27 times within the cells of all nine squares.

There is more though. Each sign appears x times in a given row, y times on the following row and z times in the next row.

x, y, z have values in either of the three nrs 8, 9 and 10. For instance, H appear 10 times on row 1, 9 times on row 2 and 8 times on row 3. Similarly, D appears 9 times on row 1, 8 times on row 2 and 10 times on row 3. Finally C appears 8 times on row 1, 10 times on row 2 and 9 times on row 3.

This is only possible if the solution is A. So, no patterns but frequencies...

Anonymous said...

I too have been struggling with this and have a different solution.

Each box contains a lateral and horizontal
Line that just features one each of the symbols.
At no time are these formed in perfect 'cross' shape (as suggested by answers B and D.
And so, A is the only solution that has both lateral and vertical lines that contain one of each symbol.
If that makes sense

Would like to hear your comments on that as a solution. Kinda simplistic I know, but maybe just as correct. ??

Anyway, I'm enjoying the book.

Anonymous said...

What about "Teeth is to Hen as Nest is to ?" (the question that appears in the footnote on page 71)?

Any ideas?

VJK said...

The answer is "mare".
The expression "as scarce as hen's teeth" means that it doesn't exist (because they don't). The original meaning of mare's nest is something illusory--or doesn't exist.

So both expressions mean the same thing.

Check it out here:

Anonymous said...

This is how I interpret the solution,

In the absence of finding a pattern, the answer has to be that no pattern is the answer.

A is the answer because of what it is missing.

None of the existing boxes have 3 of the same symbols horizontally arranged so H and F are out

None of the existing boxes have the same symbol occupying a full corner so B and E and G are out with their club corners and D is out due to the diamond and heart corners.

I also find it strangely noticeable that none of the existing boxes seem to display any symmetry. It's really hard for the human brain to avoid symmetry. which is another reason I would rule out D

This leaves A and C

This took me a bit but what you'll notice is that you can find a predictable pattern in C. If you were to add another row underneath it would be Diamond, Diamond, Club. And another row under that would be heart, heart, diamond.

So that just leaves A.

The one with no apparent symmetry or predictability.

I have this intuitive feeling that what we are looking at is visual representation of prime numbers

But this is just how my brain works,

My answer to the round manhole covers was that they are round because the hole they fit into is round. hehe.

and teeth is to hen as nest is to......(anything that doesn't have a nest)

Gpsa said...

vjk - your answer would be more persuasive if the frequencies held for the columns as well as the rows.

seaniebee the centre table has the vertical and horizontal lines you describe in the 'perfect cross shape'

the following two criteria consistent with the given tables will require A to complete the set: firstly, the table will have exactly one suit with an entry in each column (not more, not less - one suit and one suit only will have each column covered), and secondly, the table will have no more than two of the same symbol adjacent around its perimeter.

how did your son go with it?

Dave said...

Anyone make any progress on this? VJK, the frequencies idea is interesting, but then answer A is not unique - there could be a number of solutions that would match this pattern.
One thing I noticed is that there are 2 compound transformations that account for nearly all of the puzzle arrangements, and it seems to be unlikely to be a coincidence.
If you look at the 3x3 block on row1-column3 [R1C3] you can get to [R2C1] by a simple rotate left. The same applies for [R2C3] to [R3C1].
Also more interestingly, if you do a sign shift (replace HEART>DIAMOND, DIAMOND>CLUB , CLUB>HEART) then shift the cells one to the left, having them wrap around up 1 row / or around to the bottom if it's the top left cell) you can account for the remaining transformations (except R1C1>R1C2).


sign shift (H>D, D>C, C>H)

shift left 1 w/ wrap
= [R1C3]

This works for
R3C2->R3C3(our answer)

It is surprising that 2 compound transformations account for 7/8 of the puzzle progressions. Has anyone else found this and does this lead us closer to a solution?

lisafeets said...

Ok, I admit to not reading thoroughly the rest of the suggested answers but I am quite confident in my own:
First, there is a pattern but it takes a couple steps to find the solution.
1. Every grid has a column and a row with all three cards in it.
ex. R1C1 has DHC on the middle row and HCD (descending) in the right column
2. One of those 6 cards is reused, in the example it was C.
3. Label the R1C1 grid D.
4. Label the rest of the grids.
5. You find your self with 3 C grids, 3 H grids and 2 D grids... what are you missing?

lisafeets said...

ack! got confused... please read the above comment as:
3. Label the R1C1 grid as C.

... not D, duh

Anonymous said...

I put Dave's transformation (H>D,D>C, and C>H, along with a left character shift) in a spreadsheet and it worked just fine for R1C1->R1C2. I'm not sure why it didn't work for Dave -- maybe a copy error or something? Anyway, Dave's approach demonstrates an unambiguous and unique solution that matches A.

Anonymous said...

How does Dave's process work from R1C1 --> R2C2? If you do it manually, it comes out all wrong.... How did the spreadsheet do it?

I did Dave's process backwards on R1C2 in order to figure out what R1C1 would look like if there were no exceptions to the rule, and it came out as this:


Its symmetry is the only reason I can come up with why this particular square can't appear in the puzzle. (It's clearly an illegitimate reason, but I thought it might lead to something :\)

Xysuthros said...

lisafeet's solution isn't bad, but I wonder how she deals with the middle grid (R2C2), which has 3 rows having all three cards. Apparently she calls this a "D" grid, but it seems to me it could also be a "C" or "H" grid.

I think Dave may have something too, although I'd like to think there is a single transform, even if quite complex, that could explain all the progressions.

Anonymous said...

Try each cube has HCD or DCH, sometimes once, sometimes twice, sometimes vertical, sometimes horizontal. Twice where HCD appears twice in a cube the lines form right angles meeting at a corner on H.

In the possible solutions only A & D have HCD or DCH. Answer D is ruled out because HCD appears twice and forms a plus sign which is not part of the pattern.

Anonymous said...

Dave's solution is correct, the answer is a sign shift and then a cell shift to the left. Not sure if I have a newer addition of the book or whatever, but my R1C1 is different than that pictured and it works for this rule:


lisafeets said...

shoot, Xysuthros is totally right. Must have been so focused on the pattern fitting the solution that I missed the middle outlier (heh).

Anonymous said...

There is a pattern for transforming the grids. I will do my best to give a clear explanation.

I also have the following R1C1, which I will use in my explanation:


First, let's arrange the three symbols as so (the order is arbitrary):


We can use the above to establish rules for transforming one symbol to another. So, going from D to C is advancing one position, so I would label that a +1 transformation. Going from H to D is a +1 transformation, we simply wrap around to the beginning. Going from H to C is a -1 transformation. Any symbol that remains the same from one grid to the other is a 0 (zero) transformation

So, now we have the following:

D -> D 0
C -> C 0
H -> H 0
D -> C +1
C -> H +1
H -> D +1
H -> C -1
C -> D -1
D -> H -1

Now we can establish the rules used for transforming the grids. Taking the first three grids.


changes to


which gives us the following:

-1 +1 0
+1 -1 -1
+1 +1 -1

The second grid changes to


which give the following:

+1 0 +1
-1 -1 +1
+1 -1 -1

A clear pattern now emerges for how the symbols were transformed.

-1 +1 0
+1 -1 -1
+1 +1 -1

B C A*
+1 0 +1
-1 -1 +1
+1 -1 -1

Column A is modified by shifting the pattern up one.

For the second set of grids we have the following:

0 0 0
0 -1 -1
+1 -1 -1

B C A*
0 0 0
-1 -1 +1
-1 -1 0

For the third set of grids we have the following for R3C1 to R3C2:

0 -1 -1
-1 0 -1
0 0 +1

We can now predict what our rule set should be for transforming the R3C2 grid:

B C A*
-1 -1 -1
0 -1 0
0 +1 0

Applying the rules:




which is the correct answer A.

In retrospect, a fairly simple set of rules for obtaining the grids is made difficult to ascertain by using symbols instead of numbers.


Xysuthros said...

Sorry, but my first reaction to Mike's post of 7/15 is "Huh?"

He may be right, but following the explanation is daunting because of terms like "first grid", "second grid," "third SET of grids," etc.

I'd enjoy seeing this reposted with a consistent use of the "RxCy" terminology to identify which grid is being discussed.

Oh, and now after re-reading for another 10 minutes, I finally understand the explanation in the area of "a clear pattern now emerges." However, it wasn't initially clear at all. Maybe some baby steps need to be added there. Thanks.


Anonymous said...

Has anyone else tried to do this without looking at the answer, so as not to cloud your judgement? After you figure out what should be the answer, you can verify with the real answer to see if your proposal is correct. I'll post my answer using the above shortly...

Anonymous said...

All right- I've been working on this for a coupla days, maybe a coupla hours total. Here's what I've got so far...

if you label symbols thus:
Diamond =1
and you apply basic math rules, but with the set number worked with 3, ie. 1+1=2, 2+1=3, 3+1=1 (you're going back to the beginning of the series). so 3+2=2, 1-2=2, etc. Think of 1,2,3 being on a slot machine, where there are only the three numbers, and you are subtracting third rotations from it.

Given those labels, you find that for each of the rows there are three grids, and if you add 1 to the middle and right columns in the grids, then shift them both left one space, you have the next grids numbers.
For example, the first row goes like this

122 332 133
112 231 122
333 112 231

for G1C2
which is what you get for G2C1, since you did remember to shift to the left one place right?

another thing to notice is that every third grid rotates counterclockwise 90 degrees. Weird.

This next bit's trickier
Look at how C1 changes from G1 to G2 in each overall grid row. Note it.
so for Grid row 1 you get this:

122 332
112 231
333 112

between g1C1 and g2C1 above you get this:

Now that you have the -1,+1,+1 values, apply them between G2c3 and G3c3, but after you shift them all up one. ie:+1,+1,-1 now you have this

the above is g3c3. you can apply the above formula to the second overall grid row, and then the third and get the very last of the nine grids that way.
And since this pattern worked without actually looking at the answer, I'd say it's the one to go with. The frequency solution seems to work, but i think only after you've seen the answer. If you don't have the answer in front of you it falls apart on the proper placement of the symbols. I hope the above helps...

Anonymous said...

oh yeah- forgot to sign my work...

-adrian m.

Anonymous said...

It seems there are 2 different editions of the book with 2 different tests.
I would love the mathematical solution (Diamond =1, Clover=2) posted above (by Adrian),
but unfortunately, it doesn't seem to work for the problem that is on the scanned image.
For example the first row (on the picture)
is like (this is not the problem, that you usually tries to solve)
221 332 133
132 231 122
133 112 231

Starting with the first grid,
adding +1 to the to the middle and right columns transforms
but, this does not equal to the first and second column of Grid2.

If somebody has a solution for that problem that is on the scanned image, please share.

Jeffrey T. Hall said...

I have a solution that seems to work. Consider the following methodology: aggregate numerical character distribution by horizontal and vertical axes.

Here's how to do it. Take each column (horizontal) or row (vertical) and count the number of times each character appears aggregately for grid.

For example, solution A is very close to being perfectly equal when characters are expressed numerically and aggregately for all grids:

horizontal row 1 = 10h 9d 8c
horizontal row 2 = 8h 9d 10c
horizontal row 3 = 9h 9d 9c

Only off by one character in the third row.

More impressively, the vertical distribution for solution A is as follows:

vertical column 1 = 11h 11d 5c
vertical column 2 = 11h 5d 11c
vertical column 3 = 5h 11d 11c

A perfectly equal, aggregate numerical distrbution on the vertical axis.

Solution A is very close when using this methodology, but not quite perfect. That distinction goes to solution G.

Here is the horizontal distribution for solution G:

horizontal row 1 = 10h 10d 7c
horizontal row 2 = 10h 7d 10c
horizontal row 3 = 7h 10d 10c

And here is the vertical distribution for solution G:

vertical column 1 = 11h 11d 5c
vertical column 2 = 11h 5d 11c
vertical column 3 = 5h 11d 11c

In simplest terms, only in solution G is the aggregate character distribution by horizontal and vertical axes (rows and columns) perfectly equal. All other solutions fail to duplicate the pattern exhibited by solution G.

Jeffrey T. Hall said...


The image of the problem presented at the top of this page is NOT the same image presented in my copy of the book which was purchased in August, 2009. Consequently, there is some confusion created by the variance.

In my copy of the book, the upper left-most grid has a character distribution different than that of the one published here.

Here is the horizontal character distribution for solution A as it is presented on this site:

10h 9d 8c
9h 8d 10c
8h 10d 9c

However, here is the horizontal character distribution for solution A in my version of the book:

10h 9d 8c
8h 9d 10c
9h 9d 9c

I originally thought that the author of the first solution posted here had simply miscounted. Obviously, this is not the case.

I am now slightly annoyed as my contention that the book's answer was incorrect has subjected me to the ridicule and cross-examination of my wife who has repeatedly and incredulously questioned how I could possibly disagree with the answer as presented in the book.

To my wife I say this: I love you, but you were wrong--again.

Idiot said...

The solution is pretty much very easy.
There is a pattern. In both diagonals each of the three symbols is reapeted twice. Hence option A is the only right answer.

JTH said...

Dear Idiot:

Would you please explain your methodology with a little more specificity. I'm intrigued by the possibility of another valid solution. Thank you.

Anonymous said...

Dear JTH,

What I am saying is very simple actually.Taking the diagonal from the top right to the bottom left you can see that each of the three symbols is repeated twice. The same pattern seems to tend to be repeated to the other diagonal as well. You would expect each of the three symbols to be repeated three times as well. Therefore in the missing square the two clovers are missing. A is the only solution where you can actually see two clovers in the diagonal.Therefore the only solution is A.

Idiot said...

The last comment by "Anonymous" are by myself actually.

Anonymous said...

I also have for the first cell in my book:


Which would make Dave's solution correct. I'm curious to know, how many people have the puzzle in their book the way it's pictured in this post?

Xysuthros said...

Xysuthros said...

It's obvious from the comments posted that there are two quite different versions of the problem's presentation. Instead of attempting to provide solutions to the best guess at which is the "real" version of the puzzle, may I suggest that *someone* (sorry-- not me-- way too busy with a demanding job at this instant in my life) contact the publisher/author to determine the correct version of the puzzle. Without that, the best speculation and calculation are a waste of time, if I may be so blunt.

Secondly, has anyone considered contacting the creator/s of the puzzle to determine why the published solution is the right one? Many of us have put considerable thought and calculation into this, and it might be time to reveal the original algorithm that was employed to create the pattern.

Moreover, since no-one is all-knowing and flawless, explaining the original rationale for the (correct) answer might actually reveal flaws in that rationale. If that is the case, I think it most likely that some pattern, equally valid with the one around which the puzzle was contrived, might be observed by some gifted individual.

After all, this difficult puzzle is supposed to identify the very brightest intellects. Who, then, has the credentials to create such a puzzle and determine the one and only correct solution? No one can have such unerring intellect to sit in judgment of, say, the top 0.1% who are yet (possibly?) beneath him/her.

-X said...

I will be giving a solution to the version of the puzzle that is not the scanned image above. This solution extends the mathematical solution (Diamond =1, Clover=2) posted by Adrian.

For each of the six 3x3 grids in the first 2 columns, we obtain the grid to its right as follows:

1. To all nine cells, apply the symbol substitution

Diamonds -> Clubs
Clubs -> Hearts
Hearts -> Diamonds

2. Then apply the cell mapping

1 4 7 -> 4 7 2
2 5 8 -> 5 8 3
3 6 9 -> 6 9 1


vlada said...

I think that I ve got the solution :)

The whole figure is symmetrical to the diagonal that goes from upper left corner to the lower right. Let s see how:

Lets call parts of the figure fields. There are nine fields, each having nine squares. OK :)

Also, I will use C for clubs, D for diamonds, H for hearts :)

lets call fields


look at the field 1. it has three columns.

left column has 2D+C
middle column has 2H+C
right column has C+H+D

look at the field 5. columns there have the same symbols:

left column has 2H+C ( same as field 1 middle column )
middle column has C+H+D ( same as middle column of field 1)
right column has 2D+C ( same as left column of field 1)

so, the field 9 should have the same symbols appearing in specific columns ). And that is the solution D. Lets see its columns:

left column has 2D+C
middle column has C+H+D
right column has 2H+C

The same pattern as can be seen on other fields...

Lets check if it works on the rest of the figure. Fields 2 and 4 should have the same columns. Here they are:

left column: C+H+D
middle column: 2H+D
right column: 2C+D

left column: 2H+D
middle column: 2C+D
right column: C+H+D

Another proof, fields 3 and 7 should also be the same. And they are:

left column: 2D+C
middle column: 2H+C
right column: C+H+D

left column: C+H+D
middle column: 2H+C
right column: 2D+C

The same applies to fields 6 and 8

In other words, every field has one column with C+H+D, and other two columns have one double element

with closer look we can see that D is the solution. Easy way to check this is to see next:

we are looking for a field that has one column with three different symbols C+H+D, and that has one column with 2H+C, and the only one having this is field D :)

First time I saw this test was on Ashton Kutcher's twit yesterday. I tried to find solution on net, but then saw that nobody knows it.

I think that that is right. Please leave your comment @

vlada said...

I illustrated the solution that I described above

Mankel said...


The solution was posted a long time ago by Dave, that got it even though there was a mistake in the first edition of Gladwell's book.
Here you will find the correct Raven, to wich if you apply Dave's rule you will solve.


vlada said...

Hi Mankel,

Thanks for sending me the other version of the problem. I was not reading through Dave's solution since he said, if I am correct that the answer is A.

And I think that Dave said that for the other version his system works in 7/8 of the puzzle or something similar.

For the test seen on that illustration I made, correct answer is D, and D only. For this new solution unique correct answer is B, and there is no shifting nor rotating, it is quite simple counting. If you want I could illustrate this as well :)

Thanks again,

Mankel said...

Sorry Vlada, but you don't have a clue!!!

Shift hearts into diamonds, diamonds into clubs and clubs into hearts.

Then, move every cell to the left or up-right if you are in the first column of to the bottom right if it is the upper left one. That way you get the changes from the first grid (the one corrected, thats why it only worked in 7 of 8 changes for Dave) to the second, 2nd to 3rd, 4rth to 5th, 5th to 6th, 7th to 6th and 8th to A (the correct answer).

To get the 4th grid from the 3rd and the 7th from the 6th, you just rotate the grid 90 degrees to the left.

If with this instructions you are still unable to get it... I guess that says a lot about your ability to solve this kind of puzzles ;-) Plzz, no hard feelings.

vlada said...

Hi Mankel,

No problem at all. I see what You mean, but this is not working with the other puzzle very well.

Apply my system and you will get one unique solution for both versions ( your link has the solution B, mine link has the solution D )

So, maybe I have no clue, but my system works. You are right, your system works fine for this puzzle, and it could not be a coincidence that shifting and moving works, but you can not say that mine solution is bad only because you don't like it. Plus, mine solution has advantage of being correct for both versions, so there it goes :)

I am not from USA ( duh, like if my English hasn't hinted it already :) ), so I am not aware of this book, different veditions etc. Maybe they have corrected themselves in the second edition or something, I have no idea, but then they have this flaw that it can be solved using my lousy technique :)


Mankel said...

Sorry but no :)

There is a single solution: A.

The "first" puzzle has a mistaken first grid.

Think about this: the puzzle is designed to be solved quite rapidly by following a progression from left to right and up-down. I am not making this up, it is how they were designed: you have to find the next one in the progression and not a "holistic" solution that doesn't exist.

This kind of puzzles are designed algoritmically and there is not "my solution" against "your solution", and if there were equivalent procedures, both would have to conclude with the same solution.

Either you can try to understand this or remain dumbfounded.

I'm done trying to iluminate you.


vlada said...

Your last post is almost completely wrong by my opinion, and since You think the same about me, it is better to end this, since it is really going nowhere :)


Anonymous said...

A is the only grid without two or more like symbols in the top row, and in the pattern we are working from, neither of the grids in the bottom row of grids have two like symbols in the top row, so only A fits that pattern. could it just not be that simple?

Anonymous said...

i think mankel is a fu*king douchebag
if u were that clever u should have come out with dave's solution earlier.
big douchebag

Anonymous said...





Mercy Vetsel said...

That's really *(@#& annoying!

Of course it's hard to solve a puzzle that's has an error in the first step.

Anyway congrats to Dave for finding the solution:

Moving left to right (R1C1 -> R1C2), use the following:

1. Shift to left, bumping up:

123 -> 234
456 -> 567
789 -> 891

2. Substitute H->D, D->C, and C->H

When moving to the next row, rotate 90 degrees.


John said...

Simple solution.

Think in terms of connected (touching) and not connected. Row one, for instance, hearts are connected (all three hearts touching), connected, not connected.

Row 2 hearts are not connected, connected, connected.

Row 3 hearts are connected, connected, ? -> mot connected.

(hearts two connected, one not connected per row. Clubs 2 connected, one not connected per row. Diamonds one connected, 2 not connected per row.)

The only solution that fits this criterion for row three is A.

lonnie said...

Got it in 5 secs, It's A
The symbols alternate and are moving to the left with an upward bias at the end, heart to diamond, diamond to clover and clover to heart.

A complected algorithm is the next possibility after person does not notice the obvious, and in this case it was a dead give way after the watching the first two squares "move". I have a 144 IQ and yes that means I IS SMARTCHA! but seriously, the thing about abstract reasoning is the ability to notice the subtle not the necessarily the complicated, and as Mr. Gladdwell's sentiment suggests, that is not a requirement for leading and impactful successful life.

lonnie said...

Oh and my solution only works for the version in my book haha.

lonnie said...

Ok, the answer is A the using the same solution I posted to the alternate question disregarding 1 single tiny square in the top left grid(diamond to diamond vs diamond to clover). I have a seeking suspension its flawed, I saw plenty of other patterns that only pertained to 1 row or fewer than 6 squares but couldn't put them together. Its over my head or flawed, and considering the tameness of the other version I suspect the latter. said...

One rule: no position can hold more than 5 of the same shape. To solve quickly, eliminate all the possible answers that break the simple rule. A quickly stands out.


Anonymous said...

This is a "three bodies" puzzle. The first puzzle in row a.) has symbols h,c converged while d is dinverging. The question is how will they diverge? In puzzle two, row a, harts and diamonds are converged but clubs are not. In puzzle three row a, the mirror of puzzle 2's convergence is evident with. Puzzle 2 = h,d converging c divergent. Puzzle 3 =c converging and h,d divergent. Finding the mirror in the next problem sets the stage for the answer to the last puzzle.

In the first puzzle of row b, clubs are converged while hearts and diamonds are divergent. In puzzle two row b, the mirror of puzzle one occurs harts and diamonds converge while clubs are divergent and in puzzle 3 row b, clubs and hearts converge while diamonds diverge. In order to preserve the pattern of the mirror puzzle, diamonds must diverge in the 3rd puzzle of line b.

Puzzle 1 on row c, hearts and clubs, converge with diamonds diverging. In puzzle two row b, we do not find the mirror of puzzle one. Therefore the answer a, the missing mirror of convergence of puzzle two row c, is the most likely answer.

Anonymous said...

Divergence means discrete set of symbols do not touch some way. Convergence means all discrete symbols of one set touch in some way.

Anonymous said...

Just wanted to point out that solution A, can coincidentally be exactly achieved by constructing a grid composed of the single value placed in the bottom left corner of each grid, constructed in the exact order they are listed.

That is, if you take the value in the R3C1 position from each grid and put them together in the order of the grids in which they originate, they form solution A.

While this has nothing to do with the composition of the other grids, it would be my rationale for selecting A when taking a timed test and reverse engineering a quick solution...

Anonymous said...

Not sure why any of Anonymous or VJK's algorithims are necessary.

C= converging 3 symbols touch
d= diverging 3 symbols no touch
simple answer.

c / d
Puzzle1/Row a) h,c / d
Puzzle2/Row a) h,d / c
Puzzle3/Row a) c /h,d mirror of p2.

Follow the logic and the pattern through the remaining puzzles. A is the only answer. Should work for other version as well.

Anonymous said...

Whoa - I am amazed at all this.

It's far less complicated than all of these detailed explanations in this forum.

I'll give you a hint. Boxes 3-4 and 6-7 are related by rotating each symbol 3 hours counterclockwise around the center of the square.

See it now? Should be easy to work out the rest.

lonnie said...

Commenter above
I know what you mean, the point of abstract reasoning skills is noticing and stopping strenuos lines of thought. Im no prodigal but I got it in seconds and have never taken an iq test. your not aloan in ur observation.

Sorry about spelling, typing on an I phone sucks with big hands lol.

Graham said...

I have to wonder if the puzzle was purposely loaded with all of these dead-ends and partial patterns. I solved this puzzle on a flight from Orlando to Washington D.C. I recall another deceptively simple puzzle from MENSA:

I spent hours searching for codes, equidistant formulas, letter groupings, etymologies. Never made that mistake again.

Daniel said...



Hearts > Diamonds
Diamonds > Clubs
Clubs > Hearts

3 columns


Shift one square up to become

Then move one column to the left, causing all the columns to move to the left. The last column moves left and becomes the right most column.

Apply the changes (e.g Heart>Diamond)

Case closed.

Anonymous said...

Wow. All of these solutions seem extremely complicated. I got my solution (A, the correct solution) in about 2 minutes, not even kidding (I'm a 16 yr old btw). If you look at how the symbols are placed in relation to each other, you can make a lucky guess, i guess. Mine was either really lucky, or there is some reasoning behind it. If you look at the cloves in the given patterns, none of them have 3 cloves all next to each other. That rules out B E F G and H. The symmetry of D makes it extremely unlikely and awkward. C just doesn't seem likely because it is so orderly. That leaves A :)

Travis said...

Here is the real answer.

Clubs = 3, Hearts = 2, Diamonds = 1
Translate all symbols to their respective numbers

Use in clock arithmetic where:
1-1 = 3(club)

If we label each column from left to right across the top A-I.

Column G = E - 1
Column H = F - 1

If the whole square is a 3x3 stack of blocks then:
Column I top = F - A
Column I Mid = E - A

Column I Bottom = D - A

This gives you the solution without having to have even see the answer key.


Anonymous said...

The easiest answer is to look at the bottom left hand symbol in Answer A. Each symbol in A corresponds to the bottom left hand symbol of each 9 block above in the same order.The other 8 symbols in each block just confuse the eye! Hope that made sense :)