kitchen table math, the sequel: when smart is dumb

Thursday, July 21, 2011

when smart is dumb


Make each statement true by moving just one matchstick.

In Choke, Sian Bielock discusses a study in which more than 90% of adults with normal working memory correctly answered the first problem. Roughly the same number of people with damaged working memories also got it right.

Only 43% of normal adults got the answer to the second problem, while 82% of patients with damage to the prefrontal cortex figured it out.

I believe high-functioning people with autism (or a healthy loading of autism genes) will also have a high rate of success on problem number 2, but that's just me.

Better without (lateral) frontal cortex? Insight problems solved by frontal patients
Carlo Reverberi,1,2 Alessio Toraldo,3 Serena D’Agostini4 and Miran Skrap4
Brain (2005), 128, 2882–2890



TerriW said...

Turn the plus into an equals?

TerriW said...

(Though, I will say that if that is considered the correct answer, I always score in the high functioning autistic range on empathy tests, so I guess that's another data point to Catherine's thesis.)

Jean said...

I came up with that too. Hope you're going to tell us what the book says!

Catherine Johnson said...

It sure is (another data point to Catherine's thesis)!

btw, I also think that ktm has a high population of people with "a healthy does of" autism genes.

Obviously I have a healthy dose -- but not just 'cuz I have autistic kids.

I believe that normal people with a strong autism-gene 'loading' are 'independent thinkers" or contrarians or creative types....

I'd bet a more-than-moderate sum of money that you'd find people with lots of autism genes often follow what they (we) see as a rational, logical path in the face of a dominant ideology we think is illogical.

Catherine Johnson said...

Apparently my solution, which was to turn the equals sign into a does-not-equal sign, was illegal in this study.

I got number 1 right, & I couldn't do number 2.

Anonymous said...

These are closely related problems, right?

In the first one you move the 'I' on the left of the 'V' to the right, so you get 6 = 3 + 3 (VI = III + III).

In the second one you move the first matchstick on the left to be diagonal and touching the bottom of the second matchstick, so again you get 6 = 3 + 3 (VI = III + III).


Having said that, using a matchstick to make the = sign a not-= sign is also obviously correct even if this isn't the answer the test is/was hoping for.

TerriW's solution for the second one is also obviously correct even if not what was expected.

-Mark Roulo

Anonymous said...

Note that you can also turn the = sign in each problem into a > or < sign by moving only one matchstick. This should also work.

-Mark Roulo

Catherine Johnson said...

(I don't want this to show up on the "Recent Comments")

Terri's answer is the right one.

The reason you have to be a person with brain damage or a genius with autism genes to get it is that you're changing the operator instead of the numbers.

A person with a normal brain (& not enough autism genes) keeps trying to make the numbers work, which is what I did in spite of my beaucoup autism genes.

Of course, I was also a bit stuck on the obvious reality that simply turning all equals signs into don't-equals signs was the power app.

Jean said...

Mark, I also thought of the < or > sign, but I wasn't sure that would count as legal since one stick would still really be horizontal. I didn't think of the =! sign though; wish I had!

Anonymous said...

wait, are the two problems given together?

like most of these, i'd seen this before (in a martin gardner book, maybe?) so I wasn't unbiased, but my understanding was that the neurotypicals get the second question wrong because they've been primed by the first question. If you gave them the second question first, they'd get it right with much higher probability. And for whatever reason, the neuro-non-typicals don't have that priming occurring in them. To use some ideas from Minsky, when the typical mind makes a decision or solves a problem, the mind promotes that idea and depresses similar-but-competing ideas "near" it, so that it triggers on one and doesn't keep re evaluating similar results. somehow, this depressing of similar concepts isn't happening in the neuro-non-typical in the same way--whether because they aren't viewed as "similar" or they have trouble depressing, I don't know.

Anonymous said...

"Terri's answer is the right one" uses the wrong article—it should be "Terri's answer is a right one."

Sorry, it is a pet peeve of mine when people think that lateral thinking puzzles have a unique right answer. There are usually several, and good thinkers will come up with more than one. The first one for me was making it 3=3=3, but 6=3+3 is marginally ok (properly forming the V requires moving 2 matches), and 3≠3+3 is certainly ok.

Anonymous said...

I moved one stick to make it look like a V.


Catherine Johnson said...

To use some ideas from Minsky, when the typical mind makes a decision or solves a problem, the mind promotes that idea and depresses similar-but-competing ideas "near" it, so that it triggers on one and doesn't keep re evaluating similar results.

I think that's right.

I've encountered a term for something I've seen over and over again: "functional fixedness." I'll have to re-read those passages (& post), but I think that's either a term for what you're describing or it's in the same ballpark.

Catherine Johnson said...

I'm not going to take the time to read the study right now, but I think subjects did do a bunch of practice problems like the first one first.

I had the same question Allison did.

However, and I think this is Allison's point (tell me if not), practice with the first problem-type isn't 'handicapping' or 'constraining' to the person with frontal lobe damage in the way it is for people without frontal lobe damage.

Catherine Johnson said...

Note that you can also turn the = sign in each problem into a > or < sign by moving only one matchstick.

Very good!


I didn't think of that ---

Catherine Johnson said...

good thinkers will come up with more than one

But that's the point: "good thinkers" in the sense of people with high IQ & high working memory don't come up with the answers!

People with brain damage come up with the answers.

I speculate that normal people who come up with the right answer are different in some way from normal people who don't get the right answer, and I assume that normal people who get these problems are likely to have autism genes. I wouldn't be at all surprised to find people with ADHD doing better at these problems, too.

I realize I should qualify the 'autism genes' observation, given that it's distressing to think of having a child with autism....a U. of Chicago geneticist once told me he estimated that 98 to 100% of the population has autism risk genes. I don't know whether the thinking on that has changed; it may have. But when I was writing about autism research, researchers believed that there were probably lots of "autism risk" genes.

Under that line of reasoning, to actually be autistic you have to essentially win the lottery in reverse.

For everyone else, autism risk genes are harmless OR advantageous.

cranberry said...

I came up with terri's solution; my husband thought of the =! solution. None of our children are autistic.

We are a remarkably geeky family.

lgm said...

To really finish analyzing this, we must include handedness. Were the leftys significantly different than the rightys in performance?

Catherine Johnson said...


lgm always comes up with the interesting questions!

I'm going to guess that leftys will do better. (I'm right-handed, fyi.)

palisadesk said...

I'm going to guess that leftys will do better. (I'm right-handed, fyi.)

I wondered about handedness, too, because it does affect some areas of brain functioning (advantageously). I'm not only a leftie, I'm 110% leftie -- apparently there is a spectrum of handedness.

I got the first match problem immediately, like probably everyone else, and thought of two solutions for the second one -- changing the plus sign to an equal sign, or changing it to a not-equal sign -- in under 30 seconds. I'm not loaded with autism genes, so far as I know, but genes for weird ideas -- cornered the market. One valuable ability I've acquired (I don't think it's hereditary) is the ability to mentally change gears rapidly and see problems, or issues, from multiple viewpoints. I think it's an environmental survival mechanism growing up amidst a gaggle of lawyers (like, 6 of them).

Stanley Coren wrote a very interesting book on left-handedness. It's probably dated by now, but it's a good read. Left-handedness does have a strong hereditary basis. I taught for a year in a small rural community where many of the families were closely related for generations. More than 60% of the children were left-handed. That would make sense if handedness is an autosomal recessive trait.

rocky said...

Depending on how much space there is, you can change

I don't like
because that is not one statement, but a compound statement.

I don't like
because a 'V' needs two diagonals and you are only allowed to move one match.

I do like changing all the + into - and all the = into "not equal". If they don't like it, let them eat their own matchsticks.

(Sorry. I need to run with the chickens and stop thinking about flying.)

Lisa said...

More proof I'm not normal. My Asperger's boy (Mr. math) and a lefty got it more quickly than I did.