MANY people have found that a problem unresolved at bedtime seems much simpler in the morning, as if the brain had been quietly working on it overnight.

They are right, says a group of German scientists from Lübeck and Cologne, who devised a neat experiment to test the idea.

They set volunteers a mathematical test, the number reduction task, in which a string of the digits 1, 4 and 9 has to be converted into another string by combining digits in pairs according to two simple rules. The “answer” is the final number in the new string.

The test was designed to measure the “eureka moment” when it dawns on participants that there is a shortcut to the right answer. Instead of requiring seven steps, they can reach the answer in only three. The volunteers had to work this out for themselves.

The team, led by Ullrich Wagner and Jan Born, trained 66 volunteers in the principles of the test and then either allowed them to sleep or kept them awake all night or all day. Testing was resumed eight hours later and the team found that those who had slept were much more likely to work out the shortcut than those who had stayed awake.

In the sleep group, 13 out of 22 worked it out in the morning, compared with 5 people out of 22 in each of the groups who had stayed awake.

To check that this outcome was not simply the result of the sleep group being fresh and rested, a second experiment was done in which the whole trial was done in the morning after sleep or in the evening after a day awake. This time, no difference was found between the numbers gaining insight.

What these results mean is that if a problem is set and then slept on, a solution comes more quickly. Or, as the team puts it in Nature: “Sleep acts on newly acquired mental representations of a task such that insight into hidden task structures is facilitated.”

The effect is not that of having a fresh brain but of having a brain that has reorganised itself during sleep. The team suspects that the brain is able to “restructure” the way data is stored in the memory so as to make insight more likely.

“Sleep helped,” Dr Born said. “You have to have a memory representation in your brain of the problem you want to solve and then you sleep so it can act on the problem.”

Two French scientists, Pierre Maquet and Perrine Ruby, comment in Nature that the study leaves a few questions unanswered. It is not clear, for example, whether the kind of sleep associated with dreaming is needed for the process to work.

“The role that sleep plays in human creativity will be a mystery for some time yet,” they say. “But at the very least, Wagner et al give us good reason to fully respect our periods of sleep — especially given the current trend to recklessly curtail them.”

Many creative people have claimed that sleep, or dreams, have provided them with inspiration. Samuel Taylor Coleridge wrote Kubla Khan after waking from an opium- induced sleep with the poem fully formed in his mind. Some of Jules Massenet’s operatic arias were inspired by sleep, and Robert Louis Stevenson wrote key scenes in The Strange Case of Dr Jekyll and Mr Hyde after waking up.

Dmitri Mendeleev devised the periodic table of the elements after a good sleep, while Elias Howe invented the sewing machine and Friedrich Kekulé worked out the ring structure of benzene.

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