I've always thought of the notion of "sleeping on it" when faced with a hard problem or decision as a way of procrastinating working something out or taking the heat of the moment out of the equation. 

But recent research from Northwestern University finds that, when paired with some strategically employed music, sleep itself could actually give your problem-solving powers a boost. 

"We know that people rehearse or 'consolidate' memories during sleep, strengthening and reorganizing them," said Kristin Sanders, first author of the study and a doctoral student in psychology at Northwestern University, in a release. "It's also known that this natural process can be boosted by playing sounds associated with the information being rehearsed."

To hack this process, the researchers asked groups of study participants to try and solve challenging puzzles in the evening while listening to musical sound cues. A different sound cue was associated with each puzzle. Then, during that night's sleep, a program played the music associated with half of the unsolved puzzles during periods of deep sleep.

Here's an example of one of the puzzles:

On a wall outside a closet door are three standard on/off switches. One (and only one) controls a light bulb inside the light-tight, well-insulated closet. The other two switches do nothing. You can only open the closet door once, and cannot change any switches after the door is open (or re-closed, for that matter). Damaging or disassembling the door, walls, or switches is against the rules. Within these constraints, how can you determine with certainty which switch controls the light bulb?

The result was that the following day, the participants had an easier time solving the puzzles that had their associated sound cues played overnight versus those that didn't have their cue played.

"This study provides yet more evidence that brain processing during sleep is helpful to daytime cognition," said Mark Beeman, Northwestern professor of psychology and a senior author of the study, said in the same released linked above. "In this case, if you want to solve problems or make the best decisions, better to sleep on it than to be on Twitter at 3 a.m." 

The keys here are to get a good enough night's sleep that you enter the slow-wave sleep state in which memory consolidation is thought to happen, and to then manipulate your brain into focusing on the problem at hand. Working on the problem in the evening is a good start, but the rather ingenious idea of using the sound cues seems to be the bit that really makes the brain hack work. 

So next time you're trying to work through some sort of an issue at work, perhaps with scheduling, budgeting or whatever-- consider putting on some tunes or nature sounds while you puzzle over it at the end of the day, then keep those same sounds playing while you sleep. Your brain might keep working on it while you snooze and get you closer to solving it the next day.

The authors caution that their approach may only help with problems where a person has all the needed information to arrive at a solution, but has not yet come to the correct configuration. 

"For example, no matter how much sleep I get, I'm not going to suddenly figure out black holes or find a cure for a rare disease, because I don't have the necessary background knowledge," Beeman said.

By the way, the answer to the above puzzle follows: 

Turn on switch 1 and leave it on for a couple of minutes, then turn it off; turn on switch 2 and open the door. If the light bulb is on, switch 2 controls it, if it is off and warm, switch 1 controls it, and if it is off and cold, switch 3 controls it.​​​​​​

But I'm sure you would have worked that out on your own if you'd just slept on it.