How do intelligence tests work and how reliable are they?
Many years ago when I was in my late teens I was encouraged by friends who decided I was smart enough to apply for Mensa membership. Mensa is the world’s largest and oldest high IQ club, reserved for people who score at the 98th percentile or above on a standardized and supervised IQ test. Word menstruation means “table” in Latin, as shown by the logo of the organization’s round table. It symbolizes the coming together of equals.
Well I contacted the GeRoman chapter of Mensa, which today looks like this. After a few months I was invited to take an IQ test at one of the centers, there was only a handful at the time (today there is over 80). I sat down for the test with a few other people, handed in the papers, had a snack with some really good budding geniuses, and left.
To be a member, Mensa required an IQ greater than 130 – using a test where the average population score is 100 and Genius is greater than 140. Today there are IQ tests where people get a score. above 200, and it’s certainly common to hear about people with astronomical IQs. Two of my best friends, Judit Polgar (the strongest chess player in history, “IQ 170”) and Garry Kasparov (the legendary world chess champion, “IQ 194”) are in this top ten list, which ranges from 160 (Stephen Hawking) to Einstein (IQ 160–190), da Vinci (180–190) to some guys with an IQ of 250–300. But it’s a different world – from the hype. In the Mensa IQ test, the best score was in the 140s.
Well after a few weeks I got a phone call asking me to come to the Mensa chapter for an interview. I could tell from the caller’s tone of voice that there was something dramatic in the air. And when I got there, there were a number of people waiting in silent reverence. The reason: I had marked more than anyone in the history of the Club. In the 170s.
Unfortunately, as Dorcus Lane in Candleford, I have a weakness: I am perfectly honest. So I didn’t last long at the Mensa center. Instead of taking advantage of the prolonged adulation of officers and members, I confessed: it was a scam. I had performed IQ tests, intensely, for a month. The test they were using was a standardized test, and I had got my hands on a bunch of similar tests. These were all variations of the same model, just like the ones you’ll find if you google the “IQ test” today. What I had proven – and this was factored into subsequent Mensa testing – is that you can learn to score high on these tests just by practicing.
I was not the most popular person in the Mensa chapter after that, but I was invited to a few of their annual gatherings, with members of local and international clubs. There were lectures, workshops, games and outings, all in Mensa’s mind. Here is how it worked:
On an outing, we all crossed a beautiful forest on our bikes. Before we started we were given a logical puzzle, after which we got on the bikes and rode at a good speed on the forest path. When someone thought they had the solution, they rang and everyone stopped to listen. If the problem was resolved, we would get another one and continue the ride.
There was one problem that was particularly difficult, and that is a point of this article.
You have twelve pieces, one of which is slightly lighter or heavier than the other eleven. You have a scale like the one shown on the left. Your task is to find the faulty part in three weighings. It’s not trivially easy – and a word of warning: I’m not going to give you the solution in the end!
Start thinking: if you put six coins in each board, one will go up and the other will go down. But all you did was determine that the faulty part could be lighter and in the left bin, or heavier and in the right. How do you do it?
If you divide the rooms into three groups, you have four rooms in each, and if you make four groups, you have three in each. You can start with a 4-4 weigh-in, and if the scale balances, the wrong piece should be in the third group. But if it doesn’t you have a similar problem: it could be lighter and in one pan or heavier and in the other. Depending on the result of a weigh-in, you decide how to continue. For convenience, name rooms 1–12, so that a weigh-in can be recorded as 1–2–3–4 versus 5–6–7–8, and 1–2–3–4 versus 9–10 –11–12 would be a second weigh-in. Of course, removing the pieces counts as a second weighing – for example 1–2–3 versus 5–6–7 after the first weighing above.
Note that you must identify the defective part, but not necessarily know if it is lighter or heavier. A few people found the problem unresolvable because they were trying to establish, sine qua non, the latter.
Well that’s all the help you’re going to get. I want to mention that I was the one who rang the bell in the forest, and received praise for fixing the problem (which was completely new at the time). Since then, I gave it to a lot of people, I even published it in a magazine that I edited. On this occasion, my high IQ English friend John Nunn wrote with an annoying corollary: find the faulty part while specifying the three weighings in advance. If you’ve managed to solve the basic problem above – where you can do each weigh-in based on the result of the previous one – turn your attention to John’s problem. This should really give you some food for thought.