A lot of our thinking is at the subconscious level, and as LinkedIn founder Reid Hoffman points out in an interview with author Tim Ferriss, we can use this fact to our advantage when solving problems.

Hoffman’s technique for doing this is to use the relaxing and rejuvenating power of sleep to come up with creative solutions.

For example, if Hoffman is facing a business strategy problem here’s how he’ll use the technique:

Authors and entrepreneurs Jason Fried and David Heinemeier Hansson write in their book Rework that when things aren’t going as planned, our natural inclination is to commit more resources to the problem: more money, people, or time.

But that usually just makes the problem even bigger: “If you start pushing back deadlines and increasing your budget, you’ll never stop.”

Instead, Fried and Heinemeier Hansson suggest that you go in the opposite direction: cut back and do less.

You’ll be forced to make tough calls and focus on what’s most important.

They use the example of chef Gordon Ramsay’s efforts to save failing restaurants. The owners often think that increasing the number of dishes they offer will broaden the restaurant’s appeal.

But the result is usually below-average food and bloated inventory.

Ramsey’s first step is to trim the restaurant’s menu. Once the number of dishes has been reduced from, say, 30 to 10, only then does he focus on improving what’s left.

Sometimes it’s helpful to start with an existing solution, and think about other problems it could solve.

In their book Why Not?, Yale professors Ian Ayres and Barry Nalebuff call this process “idea arbitrage,” and describe how it can be applied to the following example with bookstore cafes.

Existing solution: Most brick-and-mortar bookstores have cafes that serve drinks and food to encourage customers to stay longer and buy more books.

Potential application: Put cafes in public libraries as a way to increase use of the facilities, and as a means for additional revenue beyond taxes and charitable donations and grants. Perhaps libraries could even start selling books, and then encourage people to donate their books back to the library once they’re finished with them.

One of the key benefits of idea arbitrage is its versatility: you can start with your own solutions and see if they can solve other people’s problems, or you can start with other people’s solutions and see if they can apply to you.

Here are some questions to ask to uncover opportunities for idea arbitrage:

“If you don’t make mistakes, you’re not working on hard enough problems. And that’s a big mistake.”

- Attributed to theoretical physicist Frank Wilczek