The Art of Solving Impossible Problems

When the pandemic struck, our library, like countless others, faced a predicament that felt impossible to resolve. Staff from Access Services were required to be physically present at work, while their colleagues in other roles comfortably shifted to remote arrangements. Naturally, Access Services staff asked a simple question: “How can we work from home, just like everyone else?”

At first glance, their request seemed entirely reasonable. Soon enough, though, its impossibility became painfully clear. You can’t retrieve books, oversee building operations, or handle face-to-face transactions from your living room sofa. But we tried. Discussions dragged on endlessly, producing ideas that never stuck: rotating skeleton crews to minimize exposure (which only heightened scheduling complexity without reducing frustration); creating virtual “on-call” shifts that proved ineffective, since physical tasks remained undone. With every fruitless meeting, frustration mounted.

The truth was harsh: No amount of scheduling gymnastics, digital tools, or inventive thinking could transform this inherently physical work into remote tasks. We were at a dead end, genuinely stuck.

But here’s the funny thing about impossible problems. In my experience, they rarely turn out to be impossible due to lack of resources, talent, or determination. Instead, they’re impossible because we’ve framed them in a way that leaves us no path forward. The question itself has us trapped.

Take Kodak, for example. The company once dominated photography. Yet, when digital cameras emerged, Kodak fixated on a single question: “How can we keep film photography competitive with digital?” They couldn’t. They spent millions stubbornly clinging to a vanishing market, while a revolution passed them by. Conversely, consider Netflix. Blockbuster wrestled hopelessly with another impossible question—how to lure people back into stores. Netflix simply reframed the challenge. People didn’t care about video stores; they craved convenience. Netflix flourished precisely because it refused to answer Blockbuster’s misguided query.

In his book, What’s Your Problem?, Harvard researcher Thomas Wedell-Wedellsborg observes that organizations that pause to reconsider their initial framing are far more likely to discover meaningful solutions. Yet few actually do this. Under pressure to produce immediate answers, leaders often dig in, entrenching themselves in impossible questions rather than stepping back and admitting they might be asking the wrong thing.

Eventually, in our library, we decided to confront reality openly. We told staff honestly: “Working from home isn’t feasible for Access Services. We’ve tried every angle—it simply can’t happen.” It wasn’t the answer anyone wanted. It wasn’t inspiring. But it was true. And with that candid admission, we gained the clarity to ask something deeper, something more useful: “Why does being unable to work from home feel so unfair? What’s really at stake here?”

That conversation shifted everything. Beneath the initial request, we discovered genuine feelings of inequity and disrespect. Access Services staff didn’t necessarily need remote work, but they needed tangible evidence that the library valued their contributions just as highly as those of their colleagues working from their kitchen tables.

Armed with this insight, we reframed our unsolvable question into one we could address: “How can we meaningfully show our appreciation and respect to the staff working on site?” Finally, we had a question worth answering.

We quickly redirected funds, such as travel budgets that sat unused and even funds allocated for other projects, to expand Access Services’ office renovation budget by 400 percent. But money was only part of the solution. Even more impactful was giving staff a large voice in the design and planning of the office renovation.

Taking these steps didn’t magically erase frustration or exhaustion, of course. But something important did change. Grievances about unfairness gave way to productive discussions about planning and design. Resentment was replaced by pride, complaints by collaboration, and something close to agency took hold.

Was this reframing perfect? No. There was no empirical survey, no formal metric tracking productivity or morale. I’m not offering some neat success story wrapped in a bow. Yet, undeniably, the impossible problem had transformed into something actionable. Staff felt more respected, heard, genuinely valued. They gained a measure of control over their working environment. That shift, from stalemate to tangible progress, demonstrates the pragmatic power of reframing.

Not every problem comes neatly packaged with a solution. Some problems genuinely cannot be solved as first presented. But when leaders pause, reconsider, and reframe, they open a pathway toward meaningful progress—one that replaces frustration with clarity, stagnation with momentum.

We never delivered remote work to Access Services staff. But by recognizing the flaw in our initial question, we offered something perhaps even more valuable: honesty about what was possible, genuine respect for their concerns, and tangible investments to improve their day-to-day working environment.

Great leadership isn’t just solving every problem in sight. It’s the art of recognizing when not to solve problems and choosing instead to reshape them. The strongest leaders move beyond immediate frustrations, pause to question their own assumptions, and guide their teams toward deeper, more meaningful, and actionable solutions.

Because sometimes the only way to solve an impossible problem is to realize you don’t have to.