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A night sky with a crescent moon, sleeping clouds, the letter Z and the numbers 3 5 7 9 11, beside the cover of Escape the Sleepwalking Town.

Field Notes

Sleep on It: How a Night's Sleep Can Help You Spot the Hidden Rule in a Puzzle

4 min read
  • Learning science
  • Insight
  • Study tips

Everyone knows the advice: "sleep on it." Is there any evidence behind it? There is one well-known experiment, and it is a puzzle story. Here is what it did, what it found, and how far the result goes.

The task with a secret shortcut

In 2004 Ullrich Wagner, Steffen Gais, Hilde Haider, Rolf Verleger and Jan Born published "Sleep inspires insight" in the journal Nature. People practised a number reduction task. Each trial shows a string of eight digits made of 1s, 4s and 9s. You work left to right with two rules (as described in Stickgold and Walker, 2004):

  • If two digits are the same, the answer is that digit.
  • If they are different, the answer is the third digit.
  • Use each answer together with the next digit, and carry on to the end. The last answer is the solution.

Hidden in the task is a shortcut that the people were never told about. The last three answers always mirror the earlier ones, so the second answer is already the final answer. Someone who notices can stop early. Here is one trial, computed with the rules above:

A row of eight digits 1 4 1 4 9 1 9 4 and below it seven answers 9 4 4 1 1 4 4, with the second answer, 4, highlighted as the final answer.
One trial. Working all seven answers gives 4, and so does stopping at the second.

What the study found

After training, some people slept for a night before trying again, and others stayed awake for the same time. The abstract reports that more than twice as many people gained insight into the hidden rule after sleep as after wakefulness, whatever the time of day. In the summary by Stickgold and Walker, 59% of the people who slept discovered the shortcut the next morning, while no more than 25% did in any of four comparison groups who did not sleep.

A bar chart: 59 percent found the shortcut after a night of sleep, and 25 percent or fewer in the groups who stayed awake.
The result in one picture.

Two details are worth noticing. The people were not told a shortcut existed, and training came first: the sleep effect was seen after they had practised the task.

The same idea on a number pyramid

In a sum pyramid, each brick is the total of the two bricks under it. The long way fills every brick. But some pyramids hide a pattern. Take the bottom row 3, 5, 7, 9, 11, which goes up by 2 each time. Filling every brick gives a top of 112. Because the row is evenly spaced, the top is always 16 times the middle brick: 16 x 7 = 112. We checked it by computing the whole pyramid first.

Two number pyramids. On the left every brick is filled and the top is 112. On the right only the bottom row 3 5 7 9 11 is shown, the middle 7 is highlighted, and the text says 16 times 7 is 112.
The long way and the shortcut give the same top brick.

The shortcut only works for evenly spaced bottom rows, so always test a pattern you think you see against the long way once. A pattern you have noticed but not checked is only a guess.

Modest tips

  • Do the work first. In the study, insight followed practice. Give the puzzle a real try before you leave it.
  • Stop when you are stuck. Going round in circles tires you out. Write down where you got to.
  • Come back the next day. Look at your notes with fresh eyes, and ask whether the numbers repeat or mirror each other.
  • Check the pattern. Try it on one more example before you trust it.
  • Do not stay up late over a puzzle. Leaving it until tomorrow is fine.

Where a puzzle adventure fits

Escape the Pyramid, Level 1 and Escape the Labyrinth are puzzle adventure gamebooks, so you do not read them in order: each chamber's answer is the page you turn to next. Both have 45 locked chambers. The Pyramid book also has 6 treasure rooms, and hints and full answers sit in the back. Number-pyramid locks are the core, and spotting a pattern in the bottom row is the sort of move they reward. They are puzzle books, not a course and not a sleep programme. They simply make it easy to leave a lock, go to another chamber, and return later.

A chamber page of Escape the Sleepwalking Town: a drawn street scene, the Catching Yawns rule, a partly filled number pyramid and a Next Door box.
A chamber page as printed, at low resolution. Nothing is solved.

Books mentioned

Escape the Pyramid, Level 1 (Easy) cover

Escape the Pyramid, Level 1 (Easy)

A puzzle adventure gamebook with 45 locked chambers and 6 treasure rooms, hints and full answers in the back.

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Escape the Labyrinth cover

Escape the Labyrinth

A puzzle adventure gamebook with 45 locked chambers. You choose your road, and the puzzle kind changes from door to door.

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Escape the Sleepwalking Town cover

Escape the Sleepwalking Town

A comic puzzle adventure gamebook: climb nine locked streets to the Wake-Up Pyramid, with true sleep facts.

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