Like brain teasers?

Try this one out. Take the following sequence of numbers.

And fill in the blank box. Here’s the solution:

The rules can be derived from the above example.

Take another sequence: 9 4 9 1 9 1 9.

What’s the answer?

Did you get 1?

If you understand the rules, it takes on average about 9 seconds to get the answer.

It took me 2 seconds.

*crowd gasps*

The Experiment

OK, so that wasn’t much of a brain teaser. More of an arbitrary set of rules for a dumb game (but how did I do it in 2 seconds?).

Researchers in 2004 trained subjects to solve these kinds of problems. The subjects were split into three groups:

• The Sleep Group: These lucky subjects solved 90 sequence problems before bedtime, slept from 23:00 to 7:00, then solved 300 more upon waking up.
• The Wake-Night Group: These unlucky subjects did the same thing, except they were forced to stay awake throughout the night.
• The Wake-Day Group: 90 problems in the morning. Wait 8 hours. 300 problems in the evening.

So what was the point of this?

The sequence problems took about 9 seconds to solve. However, there’s a “hidden rule” that allows them to be solved in 2 seconds.

The researchers wanted to see which subjects had the eureka moment. The graph below summarizes the results:

Nearly 60% of the Sleep group figured out how to solve the problems in 2 seconds after they had a night of sleep.

While only about 20% from the other two groups figured it out.

So this is obviously telling us that…

*drum roll*

Letting your mind mull over abstract problems while asleep greatly improves the chance of gaining insight into that problem.

Breaking News: Science Confirms the Obvious

I’m usually a bit cynical when it comes to obvious findings in scientific research. But upon closer inspection I really don’t think the results of this study really are obvious at all.

The wake-night group got the same results as the wake-day group. So sleep deprivation had nothing to do with the results. One would also suppose that the wake-day group should have gained insight into the problem since they (i.e. their subconscious minds) were allowed to mull it over during a time when circadian alertness is high.

The research tells a different story: it really is sleep itself that improves the likelihood of eureka moments.

Not to mention that the sleep group had 2.5 times the insight rate as the other group.

Math, Sleep, and Insight

It was 6:00pm and I had a 5-hour math exam placed on my desk. The subject: Abstract Algebra II. The topic: Galois Theory.

Yes, I really did have 5-hour evening exams in college. The idea was that exams should test abstract creativity, not just rote knowledge. So more allotted time was necessary.

I didn’t sleep well the night before (too much studying), so I had a huge load of sleep debt to carry. The adrenaline from the exam allowed me to stay awake, but about 3 hours in I just got stuck. Two problems left and for the life of me I couldn’t figure them out.

I went to a University with a laid back atmosphere, so I left the exam room, went into the math lounge, and plopped down for a nap on the couch. Alarm set for 20 minutes.

I knew exactly what I was doing. The college life really puts you in tune with the effects of sleep and sleep deprivation. I knew from previous experience that a nap would be the optimal use of my time. Yes, I was a “sleep warrior” back then, too.

Letting your subconscious figure something out is better than banging your half-functioning conscious mind against a brick wall.

I woke up relatively refreshed and went back to the exam room. My mind certainly was a bit clearer, though I’ve had better naps. It took me 30 minutes to figure out one problem (eureka!) and about 60 minutes more to figure out the last one.

I can’t prove whether or not I would have solved those two problems without the nap, but I really don’t think I would have. Most of the students in the class didn’t solve the last two problems, so I felt pretty good.

The Hidden Trick

So what’s the trick from the problems at the beginning of this post? How can you solve them in 2 seconds instead of 9?

The researchers of the study pre-selected only sequences where, when you fill out the bottom row, the last 3 numbers of the bottom row mirror the previous 3.

So “response 2″ is the same as “response 7″ (see above figure).

I was kinda disappointed at learning the hidden trick, since it relies on an arbitrary pre-selection of sequences. But it doesn’t nullify the results of the study because subjects were not told there was a hidden trick in the first place.

(graphs were taken from the original paper).