When Brain Damage Helps: Solution Spaces Are Constrained by Prefrontal Cortex

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eeg of brain

Different solution to #2:
IX/ = IV + V
Important to note that a slanted stick can not be taken as an "I" or anything at that so IX/ = IX or 9.
Solved it round about 3 min mark.

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Perfect just what I was looking for! .

I found these incredibly easy. I just take one matchstick from somewhere, and make the equality sign into an inequality.

It's not in violation of your rules; and as it turns out I did have major brain surgery some seven years ago, to remove a large tumour.

Okay maybe I am being daft and uneducated ,but shouldn't the answer to the first puzzle read VI=III+III ?

Interesting exercise...but I can't be the only one who noticed the "solution" to the first one is incorrect...
it should be VI = III + III, not IV = III + III

"BTW, the solutions are IV = III + III and IV = IV = IV " Uh, typo? Since when does 4 = 3+3? I also got this VI=II + IIII, if four I's are allowed. And I have another solution for #2: move the vertical of the plus sign to be a slanted slash thru the equals, and you get IV does not equal IV-IV (IV =/= IV-IV)

what you think its correct?
IV = III + III

Thanks! I fixed the stated solution. Also, the inequality solution is great; the authors didn't mention that in the rules... so I must assume you have brain damage.

(just kidding of course ;)

BTW, on the solution line IV(4) is not equal to III(3)+III(3). I'm certain that you meant VI = III + III

Are you sure the correct answer to the first would be IV=III+III

Or is the use of what appears to be roman numbers a ruse? If not then the correct answer would be, VI=III+III (six=3+3) not IV (four), etc.

So if I solved the second puzzle in less than 5 seconds, should I see a doctor?

It seems to me that an even 'better' solution to the second problem is V != IV + IV. (Where you can write 'not equal to' by crossing the equals sign with a stick taken from somewhere else.)

Was this not even considered?

how about people that are "trained" to think out of the box? do their brains assimilate brain damage patterns as suggested by the research?

Other unorthodox solutions:

- Remove a matchstick from the equals sign, add it as an I somewhere. Then you get an expression like VIII - II + III which is perfectly valid.

- Take a matchstick from a V and cross it over the other one to form an expression like IV = I X + IV. Take the X as a variable, or take it as a multiplication operator applied to I and +IV. The + is redundant but valid.

If the puzzles are this poorly specified, no wonder the "normal" people did worse.

I solved the 2nd one really quickly too... I often lack "'higher' cognitive functions like planning, judgment, and goal setting" but I am also highly artistic. Perhaps I have a mild case of ADHD, and that's got something to do with my prefrontal cortex?

Or perhaps I read too many lateral-thinking puzzle books as a child, and I've trained myself to think outside the box anyways?

Within a few secs of seeing the problem I got this solution:

VII =\ I + III take =\ as 'not equal to'
and
IV =\ IV - IV or in some combination not equating

Do you think I got severe brain damage? I got a moderate IQ of 115 in a test I took recently.

I was in a bad accident when I was 9. I fell off my bike, hit a fire hydrant, cracked my skull in three places, and was knocked unconscious. A few days later, in the ICU, I woke up. Doctors had already told my mother I probably wouldn't, and even if I did, that I'd be brain damaged. Everyone was pretty surprised when it appeared I wasn't.

Every bit of that story is true.

That said, my solution to the second puzzle was IV != IV - IV, and I reached this answer in less than a minute.

I'm asking you now, for real, seriously? Is my frontal lobe damaged? Do you think it happened when I was 9 in the accident described above? Because, honestly, that's pretty cool. I should let those doctors know they were right. ;)

I got -IV=IV-IV. Am I dain bramaged?

I never would have written this post this way if I realized how many people have suspicions that they are brain damaged.

If you don't have problems in everyday life, then why worry? Sure, you may be slower than people who haven't been concussed on neuropsych tests, but this research demonstrates that there are both advantages and disadvantages to such things!

Who cares if you are slightly slower to name the ink color of a word in the Stroop task? Or slightly slower to alternate between letters and numbers in the trail making test? And if you do care, you could always try practice.

For the second one:

IV â  IV - IV

would also be correct.

For the second one how about IV (greater than/ equal to) IV - IV. Because 4 is greater than 4 + 4. Hows that for thinking outside the box? I havent had brain surgery, but I had an extremely high I.Q. when I was young.

I came up with the inequality answer too as I read the blog post. Maybe the actual paper rules out the inequality where as here we were unintentionally lead to it.

@MoonShadow - for those people...We get them a bigger box.

I solved the second one rather quickly and came up with the expression

IV = IV = IV

My answer to the second one was "IV + IV + IV", which is a valid mathematical statement. But I suppose if it had been described as a "valid mathematical assertion" then my answer would be incorrect.

I disagree that the inequality sign is valid - you don't really see inequality sings in equations, except when a point is being made as in an incorrect answer to a problem, etc.

I didn't get the second one though.

I agree that the inequality sign must have been disallowed in the protocol but accidentally omitted from the writeup. Otherwise it is a valid solution to almost any matchstick problem, and thus does not require "out of the box" thinking (the real point here).

alternate solution to the first one: VII = IIIIIII

For the second one, take the horizontal bar from the plus sign, and move it up to make a square-root sign. Then it says:

IV = I sqrt I IV

I interpret that as saying:

4 = 1 * sqrt(1) * 4

I don't have gross brain damage, but my personality is in the schizotypal direction (don't know the magnitude). And some researchers at Vanderbilt (IIRC) showed that schizotypal subjects had more creative solutions to problems than either normals or full-blown schizophrenics (who did the worst).

This is stupid. I solved them both in about 10 seconds.

You can blow me if you think I'm brain damaged.

VALID mathematical statements:

VII > II + III

IV < IV + IV

aren't they?

Rats... I thought the solution was this:

IV = IIX - IV
4 = 8 - 4

Granted that is technically moving 1 and fiddling with two... but isn't IV = IV = IV fiddling with the horizontal in the + to move it up or down?

why isn't the answer to #2 VI = III + III? am I missing something here or is this type of "multiple correct answer" kind of problem?

never mind about my last post - obviously I didn't read the problem description beforehand

I also found them both particularly easy. Keep in mind they are dealing with averages here. In my case, my INTP brain (Myers Briggs) just flies right to the answer.

For the first one, I turned VII = II + III into VII = IIIIIII. I suppose that's not good enough, but it seemed valid at the time.

yeah, the directions ought to read "Can you move a single matchstick to form a valid mathematical equality?" I did the same trick as Duae.

For the first one, I got another unorthodox answer: take the crossbar from the plus sign and place it erect to form: VII=IIII III. I got the double-equality for the second.

As it happens, I know I'm brain-damaged! ADD diagnosed early on, plus some mysterious but disruptive issues, which I recently identified as Non-Verbal Learning Disability (a relatively mild autistic disorder). This condition makes it difficult for me to learn or interpret certain things, notably social cues. The flip side is that I routinely pick up on things that normal people "look through".

The human brain is resilient beyond the dreams of any human computer-maker. Even in the face of overt brain damage, we can do amazingly well at carrying on. Subtle damage and developmental hiccups can still cause handicaps, but they can also yield new and unique abilities and perspectives. This biologically-fed diversity of abilities and behavior is one of the basic strengths of humanity.

Got the IV != IV - IV solution in less than a second, does it mean I'm lobotomized ? :)

I got a different, simple answer to the first one: 5 = 1+1+3

y, i also immediately came to VII â  II + III and IV â  IV - IV (and every iteration of).

but then i thought that maybe that was too cheeky. i thought the answers were prety easy myself.

i wonder if the fact that i do some coding made it easier as i am constantly doing variable mathematics. i saw these more as variables than i saw this as a numerical operation.

Rex B: Basically this means that if you had brain damage atleast you would be able to comprehend the instructions. Figuratively speaking of course. "Can you move a single matchstick to form a valid mathematical statement?" Rex B says, "NO!"

Uh oh. I immediately got the right answer to the second one. The first one actually took me a lot longer.

I have a very funny proposition...

we can actually measure how much a community is affected by the cybercondria when exposed to a blog post that has scientific foundations of proof = =...

But on the more serious side, i think they is a serious methodological flaw that can be seen from the discussion here. There are just too many permutations of answers. How do you actually determine which ones are actually "thinking in the box" and "thinking out of the box"?

ummm maby its just me but it did not say that they had to be equalities, so couldent you just move one of the sticks in the = sign and make it into a + sign, if ao ahould i see a doctor

Doh. I assumed you weren't allowed to rotate the match you moved. That would have been a much harder problem to solve. 9 = 4 + 4 or 4 = 4 - 3 was the closest I could get that way :(

wouldnt VII = IIIIIII Also be valid for the first one?

That's an incredibly poorly defined question.

Discarding placements that would render the sticks into mathematical nonsense or breaking/bending a stick, other mathematically correct solutions off the top of my head:

N = IV + IV (and variants)
IV â  IV - IV (and variants)
IV â  V + IV (and variants)

Easy, I did in some seconds.
a) VII ≠ II + II (7 is not equal to 2+2)
b) IV = IV = IV (4=4=4)

for the first one, i got |V| = II + III
and people, stop using the ! before the = for an inequality.
i kept trying to figure out why you are thinking that the factorial of 5 is 8.

Clearly andy doesn't program ^_^

With a little Googling, I found a similar study that included the second matchstick problem, Oellinger and Knoblich 2003 (pdf), and their rules were:

1) All problems could be solved by moving 1 stick.

2) That sticks could not be removed.

3) That the only valid symbols were Roman numerals and the arithmetic operators "+", "-" and "=".

That eliminates the inequality answer (which is also what occured to me).

Nice work Benjamin! (That looks like a great paper too). I updated the post to reflect this new (but obviously intended) constraint on the problem space.

Figured out another solution for the second: Xll-V=Vll.
Does that make me extra brain-damaged?

I got one better
IX = VI + III

IV = I \/ + I \/ <-- move the last stick to cross the second stick.

IV = I + I + II

Um... This sounds ok and all but I figured the second one out in almost the same time as the first, and I've never had prefrontal lobe damage... maybe there's something wrong with me?!

Actually I'm really good at thinking outside the box, so it was right up my ally.

Moonshadow made the following point: "But on the more serious side, i think they is a serious methodological flaw that can be seen from the discussion here. There are just too many permutations of answers. How do you actually determine which ones are actually "thinking in the box" and "thinking out of the box"?"

In fact, I had the same issue when I worked on my dissertation way back. I had defined ideas generated in a brainstorming study as 'Paradigm Preserving' and 'Paradigm Modifying'. My original plan was to create a continuum from completely PP to various shades of PM. Unfortunately, the PMness of an idea is entirely dependedent on where you begin. And this is highly sensitive to one's upbringing and the cultural space in which one is embedded. I have, since, been very wary of claims made in studies concerning 'out of the box' thinking.

missing the obvious?

VII = VIII - I

my solution immediately and i have no know brain damage (do drugs count?)...

Not to point out the obvious, but we're not age- and education-matched to "patients with focal brain lesions to the lateral or medial prefrontal cortex". For that matter, we're not going to be representative of "healthy subjects" either. I for one have had experience with similar matchstick problems, and more generally with "outside the box" puzzles. Which means many approaches are no longer outside the box for me:
- interpreting the modified equations upside-down
- one side of a V not being slanted.
- interpreting parts of the equations as words.
- changing the location of the equals sign.
- changing the operations.
- making a term negative.

Now as it happens, the assumption guarding the second solution wasn't in my toolkit of assumptions to check. But it was in the spirit of them, and I don't think my previous experience was useless.

While stoned, I solved both puzzles by removing the vertical match from the +, so the equation in my mind changed from:
whatever = whatever + whatever to:
whatever = whatever - whatever.
It didn't concern me that the numbers wouldn't work out correctly. Or that the instructions said move, and that didn't necessarily allow me to remove a match.

The provided solution for #2 requires the moving of two matches... the horizontal one moves up, and the vertical one rotates into place.

So - it may be that you can't get that solution if you are a pedant as well as brain damaged :)

damn, I can't do this one! I blame my job for tiring me out and fast food which makes me droooowsy!

THE SOLUTION TO THE SECOND PROBLEMS ARE TWO EQUATIONS:

IV = IV = IV,
"4 = 4 = 4"

There are two = , so there are two equations!

It took me a while to get the answer because I was looking for a single equation. So you have to change the specifications of the problem.

Another solution to the second one

IV = IV + IV

becomes

IV ≠ V + IV

In case that symbol doesnt display properly in your browser, that symbol is "not equal to"

My answer to both questions was "Yes"

solution to second is
V /= iV+iV

five not-equals 8

I also got the inequality, and searched for another solution, which I got by turning the picture 90 degrees:

\
/
_

+

\
/
_

=

_
X

That is,

2
+
2
=
4

oh no, it took me less than 10 seconds each to figure out.

Hmmmmmmm. So now thinking outside the box = brain damage?

More junk psychology.

I think it goes without saying the author used poor examples for the illustrative effect desired.
Just because correct answers were garnered quickly by non-dain bramaged individuals shouldn't take away from the impact of the study.
GWB is going to declare martial law and suspend the elections - watch and see those results!!

There is only one real solution for each of them.
Only mathematical functions allowed are : + - =
IF "not equal" function was allowed, along with some others, there would be multiple solutions.
Also, number four in roman numerals is "IV" and not IIII.
There is really no point in doing these, if you're not about to read the rules :)

The obvious mathematical solution to the second one is IV = IIX - IV. Remove the vertical component of the addition sign, cross the second slanted match in the first IV after =, and you are left with two vertical matches (though one is slightly slanted, that's irrelevant) and the numeral X. Or, 8. So 4=8-4, which is mathematically correct.

the first one could also be answered as

VII = II II III

turning the + into 2 single 1's

Drew, 4 is not greater than 4+4
Antonio, Vincent Delgado, Tom, Andy, and Doug Napoleone - You are only supposed to MOVE 1 MATCHSTICK.
Doug, technically VIII is 8 NOT IIX.
Ariox, last I checked -4 is NOT EQUAL to 4-4
I did this puzzle in about 20 seconds with the IV=IV=IV .... But as a programmer that is not abnormal.

I figured both out then read the text. I hope I don't have brain damage. O.o

XII = VI X III

this works too...i dont have brain damage that i know of

Maybe I'm brain damaged, but I think not. I simply systemized the problem, exploring all the options. Moving one stick means that you can only change one side of the equation. There was no single stick move to make the number on the left equal eight and and no single stick move to make the numbers on the right equal four. So the answer had to involve changing one of the two math operators. I wasn't clever enough to see that I could turn the equals into an inequality, so that left only the plus sign on the right. Making it a minus wouldn't work, making it an equals worked perfectly. It was a simple matter of elimination, aiding by the simplicity of the move only one stick rule. Testing all the two-stick options would have been far harder.

There's a classic Star Trek episode where Spock does something illogical, the ultimate 'sin' for a Vulcan, and defends his action by pointing out that no logical solution would have worked in that situation. This is similar. No 'inside the box' solution with the Roman numerals works, so logic dictates moving outside the box, changing symbols rather than numbers.

IV=VII-III

Solved it within a minute as XII - III = IX. Have no drain bammage as yet known.

IV = IV + IV
can be transformed into
VI - III = III

Hmm...It seems to be very easy for me....I think I have a trouble in my brain.. :|
Simply moving one matchstick both two question.

VI = III + III
VI = VI = VI

interesting....

has anyone mentioned VV-IV=VI? cuz if im not mistaken that is correct

To the first post the rules state that the only symbols you are able to use are + and =. If you read the whole thing before making a comment you would know this. You didnt pass that 4th grade test, that stated in the directions to not take the test, but to simply put your name on it and return it to the teacher, didn't you?

Agnostic, you rock!

Perhaps those of us that got both puzzles within a short amount of time are just a little better educated and quick witted than those that didnt.

thanks for this article

It would be easy if you could use ≠

As another poster stated above:

iv=iv=iv is not an equation. It is *two* equations.

In this sense "thinking outside the box" means "not following the rules as stated."

I don't find it any less wrong than the commenters who feel "!=" is allowed ("!" is not a valid symbol according to the set-up)

I think a more correct solution to the second problem sould be:
IV=I-I+IV

Poorly worded puzzle.

An equation is defined as TWO equivalent expressions, not THREE. The second "solution" is NOT an equation. Most people are going to attempt to logically solve it by forming equivalent values on either side of the equal sign. To claim the answer has three values is wrong.

It's like that annoying kid who makes up a new rule in the middle of the kickball game.

"I think a more correct solution to the second problem sould be:
IV=I-I+IV

Posted by: macgiorgosgr | June 27, 2007 12:44 PM "

doesn't follow the rules

I solved the second by moving the vertical match from the plus to the middle number and breaking the first V. Then it would read III = VII - IV (3 = 7 - 4). I'm not aware of any brain damage since I've never had surgery nor received any major trauma.

I've posted a comment on "the frontal Cortex" on how i think the experiment might be too premature one to actually explain gambling behavior in persons with brain damage...

but on this case, i think maybe the brain damage does not constrain the solution space, but instead it might be determining the problem solving strategies that are adopted by the individual.

let's say the person only has these few strategies he has learned. So he'll probably use these learned strategies, which he is more good with. Maybe the PFC plays a role in selecting the strategies, so he is less likely to "this outside the box".

As you can see from a few of the previous comments, some people have had no problem solving it, instead some have had even faster rates, and even more creative ways to do it! So maybe the PFC is the one that brings focus on the learned strategies (the ones that you are best at) to solve a problem. The brain damage might be causing a loosened grip of the PFC, thus the individual might be able to access strategies that are "outside the box" at a faster rate.

That's what i can manage to summarize from the post here, and the gambling post at the frontal cortex.

What do you guys think? @@

An equation has only one "equals" sign, so I have to agree with the criticisms above: 4 = 4 = 4 is two equations. Instead of asking for a "valid mathematical equation", you might want to change the wording to "true mathematical statement". But even then, one could argue that the supposed answer is actually two statements.

you have to move two on the second one - move up the minus and then move the other one used to make the +

Alternate first solution
from VII = II + III
to VII = IIIIIII
although IIIIIII is not an accurate roman number

Except an equation, by definition, means that the two sides of the expression must be equal. An expression with a "not equal" sign is all an inequality. Therefore, the inequality solution is incorrect.

Not that I think the official answer is correct either.

Alternate first solution
from VII = II + III
to VII = IIIIIII
although IIIIIII is not an accurate roman number

As far as I know I've never had brain damage/surgery of any kind... I managed to solve the last one in about 10 seconds. For comparison, I've always been an honours student, but I much prefer the arts to sciences (although our school systems rank students on how well they perform in the sciences/math which is a topic I could bore everyone to tears with in its flaws). I'd like to think that my quick success has more to do with the visual rendering abilities I posses that make me a decent artist than with some kind of failure to interpret situations "logically."

I lit the one match, moved it over the others, and watched as they all turned to ash. from there I decided that I could no longer solve the problem. I was too busy putting out the fire.

I found it trivially easy, and I really can't imagine any decent programmer or even anyone at all with a decent math background failing to easily solve the second puzzle. Does that mean programmers all have brain lesions?

Great Post Chris!
I too had blogged earlier regarding some studies that showed how brain damaged patients can be good at gambling . People interested in this article and in the Frontal Cortex post my like to check that link too http://the-mouse-trap.blogspot.com/2006/09/how-to-maximise-your-bets-be…

Modular mathematics for the second one - remove one matchstick, then replace it just as it was. Think of it as a clock with only four hours instead of twelve - moving the hands completely around once is equivalent to doing it twice.

unfortunately, an equation only allows for 2 elements (x=y), so the second test is invalid. It would be classified as a statement, but statements are disallowed in the rules.

Both puzzles are rather easy and their solution does not require an outside of the box thinking, IHMO.

OK, Yishay, that's fine, but then what's your explanation for why healthy adults are outperformed by frontal patients?

So MANY people failing to read the instructions is a REAL worry!

The rules clearly stated:
"No sticks can be discarded, an isolated slanted stick cannot be interpreted as I (one), and a V (five) symbol must always be composed of two slanted sticks. UPDATE: The only valid symbols are Roman numerals and "+", "-" and "="."

I figured out the first one... no hope with the second one!
I have had brain traumas and lost some memory. But it has never worried me because I simply don't remember that I've forgotten anything!

Didn't this test reveal that most people actually create a further level of difficulty by assuming the problem cannot be solved in a simple manner?

A rewording of the rules will make the stated solution to problem #2 closer to being "correct":

For each of the invalid equations below, try to move a single matchstick to a different position so that the matchsticks now form only valid mathematical equations? No sticks can be discarded. The only valid symbols are Roman Numerals and "+", "-" and "=". A slanted stick cannot be interpreted as I (one). Symbols for V (five) and X (ten) may only be comprised of two slanted sticks. The vertical and horizontal spacing of the sticks does not need to be exact.

Hmmm, I solved the second problem in under 5 seconds. Hope my brain is OK! Seriously though, I suspect the reason is that I program in Java, which allows variable assignments in the form:

a = b = 17;

so I'm used to seeing that kind of layout, whereas school maths has made most of us principally familiar with equations with just one 'equals' sign.

My lobe must be very intact.
Even after seeing the solutions it took me a second to understand them, and I minored in mathematics in college!!

IV=IV=IV was almost instantaneous for me as a reaction to the second challenge. It isn't a math problem, but an identity statement, but it is perfectly valid logic.

Did the non-damaged group have experience doing mathematical proofs? Read much science fiction? I'm trying to figure out the difference between me and the majority of people, and brain damage isn't the answer.

that is soooo weird. I think my mum must have dropped me on my had as a child - lol!!

I solved both of those very quickly. I've been told I have a high IQ. I tend to believe living with L-Temporal Lobe Epilepsy for 42 years has inspired me and others with similar disorders to work harder to keep up with the average.

I found these to be very interesting. It does not take much to slove them.

If the puzzles are this poorly specified, no wonder the "normal" people did worse.

who ever came up with this is retarded.

The question isn't really defined very well. What constitutes "moving" the matchsticks - changing position? Rotating?
Also, equations have only one equals sign. So you're thinking of ways to solve the puzzle without creating another equals sign - which is why you don't solve the puzzle. It's not just an equation - it's the same equation written twice, or two equations depending on how you look at it.

First puzzle took long enough to tilt my head, second I moved that matchstick the second I laid eyes on it. Then I read the rules. Then I read the article. I came here looking for something else. Thanks, fun! And, yes, had blast trauma years ago with many concussions through the following years. Socially unacceptable peabrain, too! IQ tests no longer qualify, or I register as legally retarded, and I went to university lectures in middle school (12-13). Just lost my speedy killer sudoku skills with last concussion, so this seems to contradict the puzzle, or is sudoku more "in the box"? Any ideas? ps- have tried to correct missing words, etc, hopefully I'm making sense here! Lost some language skills from other areas... took me a long time to write this!

Ok so I am trying to figure this out...HELP!

I can not figure out this riddle for nothing! Can anyone help? You have 5 matchsticks, you can only move one over to the other side of the equation in order to make it equal...

\/I = II

(The "V" stands for 2 matchsticks and the "I" are each a stick, on the paper they look like roman numerals but they may not be) Help me please!!!