Here is an excerpt from an article written by Saj-nicole Joni for the Harvard Business Review blog. To read the complete article, check out the wealth of free resources, and sign up for a subscription to HBR email alerts, please click here.

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Have you ever noticed how, against all odds, someone, somewhere, manages to discover a solution to an insoluble problem through sheer intuition?

I’m thinking about this because my house nearly burned down about 5 months ago. We managed to escape with our lives and to save two of our indoor cats, but our third cat, Bella, the shy one who always hid, went missing during the chaos. While part of the house was still standing, we couldn’t live there, but my family and I were there every day and every evening — looking for Bella, putting out food, calling to her. Marlis and I went through everything that was left, with a fine-toothed comb. Kathy came home from Europe early and scoured inside and out. Andy searched, listened, and stood ready to open walls and floors.

The fire demolition team took up the search. We placed “missing cat” posters around the area. We alerted the animal shelters. Kathy even slept one night on the floor in the uninhabitable house hoping to hear her. In an act of sheer desperation, we hired someone who turned out to be a scammer in the form of “animal tracker” who was very happy to take a lot of our money and promise us that Bella was outside, alive and ready to come home. No cat.

Two weeks after the fire, I felt sadly sure that Bella was gone. But Kathy felt differently. She had the strongest sense that Bella was still alive. Three days later, she felt a strong pull and went into the most damaged part of the house. “Bella”, she called. She heard the faintest “meow.” She called again, and heard a tiny sound. She ran to get the flashlight, saw Bella stuck in the floorboards, and called for help.

Beyond any rational explanation, Bella survived the weeks of demolition, and was barely alive — but she was alive! Andy got her out. We rushed her to the cat hospital, where she was rehydrated, fed, and restored to health.

This isn’t just about cats. I was working with CEO of a manufacturing company when suddenly an overseas employee was missing, and feared taken hostage — maybe he was dead. The firm did everything that was rational, logical, and practical, including immediately putting many expensive experts on a team, working with governments, police, and the media as they tried to find him. As the first few days worn on, the most junior person on the CEO’s staff had this bizarre idea. He suggested they look in a very unlikely place — on their own property, but under the main building. This was based on “nothing but a hunch”. And it turns out that there he was — he has slipped and fallen in a most unlikely way. He was unconscious, but he was still alive.

When Kathy told me she still thought Bella was alive after more than two weeks of being missing, I did not stop her with my logical arguments about how we’d already tried everything. Instead, I urged her to follow her hunches. This is counterintuitive, because most of us disregard what we can’t see, measure, or prove. And most managers don’t listen to people with hunches.

Think about other “hunches” — from the people who had a feeling that the Chilean miners were still alive, to those who tried to warn BP about the unstable well in the Gulf of Mexico before it exploded. Creativity, says author Steven Johnson, often springs from what he calls the “slow hunch” — the incubation of ideas that, when colliding with other people’s ideas, build into stronger and stronger hunches, which lead eventually to a breakthrough idea.

In my view, it’s critically important for managers and leaders to nurture such hunches and create and environment where they can yield fruit. What about you? Here are three really important questions and we’d love to hear your thoughts: Have you ever had a moment when intuition — yours or someone else’s — saved the day?

As you come back to work after summer holidays, what is one intuition you should follow, not disregard?

When it really matters, and logic, expertise, and known answers fail, will you remember Bella and turn to those whose hunches can turn the impossible around?

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Saj-nicole Joni, chief executive of Cambridge International Group, is a confidential advisor to CEOs and top executives worldwide. She is the author, with Damon Beyer, of The Right Fight.