Bad Mensa puzzles

I have some questions about Mensa. It’s an organization founded in 1946 whose membership is restricted to people scoring in the 98 percentile of IQ. But IQ is a scientifically dubious concept associated with eugenics and racism, and many people who would qualify for membership probably have better things to do, so I wonder what their membership looks like. I also wonder to what extent it’s just a thing that people sign up for and forget about–maybe subscribe to a newsletter, buy a thing or two from their store.

But this story is more personal–and more petty. It’s the story of why I disliked Mensa from a fairly young age, even though I most certainly would have qualified for membership. See, I received a lot of puzzle-based gifts, and I always thought that those with Mensa branding were the crummiest of them all.

75 Number Puzzles

This article was made possible by my rediscovery of one such Mensa product. The product is called Mensa Number Puzzles, copyright 1995.* It consists of a deck of cards with bright solid colors. The cards contain 75 puzzles, followed by the solutions to those puzzles.

*The ISBN is 0-8118-2263-X. When I looked that number up, I found a product titled “Mensa: Mighty Mind Benders: 75 Number Puzzles”, published in 1999, which doesn’t match what my copy says—but it’s apparently otherwise identical.

In this sort of puzzle, first impressions are very important. The puzzle writer needs to build trust with the puzzle solver. If the puzzle solver does not trust the puzzle, then they are not going to be willing to spend a lot of time solving the puzzle, because it might turn out the solution was bullshit all along. Furthermore, since solutions cannot be easily verified without looking at the solution cards, the solver may prematurely suspect that they already have the answer, however unsatisfying it may be.

So let’s look at the very first puzzle in the deck.

A puzzle showing two clusters, each with six numbers radiating out from the center, which contains a question mark.

I think this is fair use, but out of respect for copyright, this is the only image I’m sharing.

This puzzle asks you to determine what number goes in the center of each cluster. That’s it.

The first problem with this puzzle is that there’s no obvious way to verify a solution if you have one. A better puzzle design would show two completed clusters, and followed by a third incomplete cluster. When you find a pattern that successfully predicts the first two clusters, that’s a sign that you solved the puzzle and can check your answer.

But since the puzzle does not provide you with any completed clusters, the solution is severely underdetermined. You could hypothesize, for instance, that the number in the center is equal to the sum of all the other numbers. There is nothing in the puzzle to contradict this, except common puzzle conventions about “elegant” solutions. It’s not good to rely on puzzle conventions in the very first puzzle, because puzzle conventions vary from author to author, and any puzzle needs to first establish its own conventions.

So the puzzle solver is left to guess that there is some pattern among the six numbers in each ring. Your thought process might go: How does 48 go to 7 to 120? Is it significant that the pattern alternates high and low in the first ring, and is increasing in the second ring?

But if you had any of these thoughts, they were all dead ends. The solution only has to do with opposite pairs of numbers. If you take numbers on opposite sides and divide them into each other, you get a common number, and that’s the number you put in the center. And there’s one exception to the rule, which is that 17 and 7 get added instead of divided. I’m not saying this puzzle is impossible, and you’re welcome to brag about figuring it out before I explained it. But it’s definitely not a good puzzle.

After spending four paragraphs explaining why the first puzzle is bad, I’m going to spend far less time talking about the other 74 puzzles. They’re not all bad. But there are definitely enough bad ones that it engenders a lack of trust, and the lack of trust weighs down even good puzzles. The second puzzle assigns number values to names and asks you to evaluate a new name–the solution involves converting letters to single digits 1 through 9, and adding the digits up. Another puzzle provides a list of 25 numbers attached to arithmetic operations, and asks you which five numbers will equal 1–the search space for this one is just unreasonably large. Another puzzle has a hundred digits scattered in a square, and asks you to draw straight lines to create regions of equal sum–again, the search space is too large, and am I supposed to draw the lines directly onto the card??

The puzzle enthusiast’s case against IQ

I have no idea what led to the creation of this crummy product of the 90s, but I’m going to speculate and talk shit about IQ.

IQ is usually measured with Raven Matrices, which are a sort of symbolic pattern-matching puzzle. But Raven Matrices are not good puzzles, nor are they intended to be! They’re intended to measure something. A good puzzle isn’t there just to divide people into those who can solve it and those who can’t, a good puzzle actually provides a positive experience to those who attempt to solve it. Leave it to the organization founded on IQ to misunderstand the basic point of a puzzle.

Mensa puzzle products generally market themselves as being a form of mental exercise. In general, I don’t like puzzles that are marketed this way–it’s like tea that markets itself as being good for your immune system. It’s puzzles for people who don’t like puzzles for themselves (or who can’t admit that they do), and just see puzzles as means towards reaching some other goal.

There’s also an underlying contradiction here. IQ is supposedly an objective measure of innate intelligence, something that can’t be improved. But here a high-IQ society is selling products that help you “exercise”, with the implicit goal of improving or maintaining your IQ. As a puzzle enthusiast, I long suspected from a young age that IQ was a sham. Here I was, having spent a lot of time solving puzzles, so of course I would perform well on a puzzle-based test. It was never measuring something innate at all, it was measuring something that I had unintentionally specifically trained myself for.

General disclaimers: Perhaps the Mensa puzzle products from my youth were not a representative sample, or perhaps Mensa has gotten better at designing puzzles. I’m sure many Mensa members are good people, and that some are properly skeptical of IQ. But IQ is bad and I will always be suspicious of an organization based on it.


  1. says

    I’ve long felt that Mensa’s purpose is to convince people that they are geniuses, leading them to join the organization and become dues-paying members.
    Back in the 1980s I took a practice Mensa test in one of the popular science magazines, part of an ad campaign they were doing then. I scored off the charts, IQ above 150, great candidate for Mensa.
    Yeah, I don’t think so. I mean, I’m fairly smart, but let’s be real here.

  2. Rob Grigjanis says

    I never wanted to be part of any club that would have me. (is that one of Groucho’s?)

  3. says

    i knew of a couple that met on mensa forums and got married. i was suspicious the lady – from conservativeland usa – was into the dude because of eugenics – them being in mensa in the first place, plus the guy was 6’2″ blonde and blue-eyed. joke’s on her if that was true. they couldn’t have children, and even if they did, he’s a walking talking pile of genetic health problems.

  4. Pierce R. Butler says

    A long-ago neighbor of mine who moved around a lot joined the local Mensa group wherever she found one.

    By her report, they differ widely: drinking societies, family-activities clubs, sex groups. None existed where we co-lived, and I’ve never felt much urge to check them out elsewhere for myself.

  5. says

    Hey, if Mensa members use it as an excuse to join a meetup group, good for them. Meetup groups are cool. I’d rather join a board game meetup, but some folks aren’t into that.

  6. billseymour says

    Years ago, I squeeked into Mensa based on SATs (tests that high school seniors took as part of the college admission process) with scores totalling a bit over 1300 (98th percentile…just).

    The local group in Pittsburgh, PA, was lots of fun. We did some spelunking, walked around some museums, things like that, and had interesting conversations about them.

    When I moved back to St. Louis, MO, I found a local group who mostly wanted to talk about how smart they were. I let my membership expire.

  7. says

    Back in high school I took the test to get into Mensa, and got in, but then I was too shy and awkward to actually go to any meetups so I cancelled the membership after a few months. From what I remember from reading their magazine, there was some elitism- but maybe I specifically noticed that because I also kind of thought like that back then. Like it was about being different and smarter than other people. Like you said about their puzzles being more about determining who’s smart enough and who’s not, rather than being for fun.

    I also did a lot of contest math back in high school, and that was a big part of my identity- but it turns out in the real world as an adult, those kinds of skills don’t matter as much- in the real world, getting a real job, it’s important to be able to work together with other people. For example, at a job interview, it’s not about being good at the job, it’s about being able to convince the interviewer that you’re good at the job, which gets into the complicated skill of talking to people.


    I’ve always been able to score absolute top numbers on SAT type tests, and didn’t consider that as making me better than those around me. I passed on MENSA in high school because it stank of elitism. It is interesting to hear the varying nature of groups people actually joined. I agree with Perfect Number that success in the real world is a different set of skills, albeit overlapping with the testable stuff.

  9. says

    MENSA seems to be a club for people who think they are smart. Thinking you are smart is not the same as being smart. For a start, they aren’t smart enough to save themselves the membership money …..

    Also, it’s not clear that the test isn’t testing strongly for comprehension of the phrasing of the question — there may well be cases where a person would be able to solve a different real-life presentation of a problem with the same underlying mathematics. Some people are fine with just a description; but many need a picture, or even the actual thing in front of them, to understand it fully. It’s no good knowing the answer if the question is asked in a language you can’t speak a word of …..

  10. says

    I was invited to give a talk at a national MENSA conference. It was…disappointing. The attendees generally weren’t that smart or accomplished, but loved to talk about how smart they were.
    Then they paired my talk with one by an intelligent design creationist — there were lots of ID people there. I guess putting “intelligent” somewhere in the name of your philosophy was sufficient to win MENSA adherents.

Leave a Reply

Your email address will not be published. Required fields are marked *