Problem-solving: step by step

As the resident household chemist, my college-age kids have routinely asked me to check chemistry problems for them—and I’m happy to do so. That said, sometimes I get stuck, and this is not fun for them or me, after all, I am expected to be the domain knowledge expert! Recently, we had a particularly challenging problem come up, and neither of us was able to get the correct answer.

When I was a student (many moons ago), there were answers at the back of the text for the odd exercises. If you were lucky, there was a solutions guide for all the practice problems. With online materials, every answer is available, and many have examples on how to solve the exercises, and for this particular case, when the solution was requested, we were presented with a single equation that incorporated all the information provided in the problem with the unknown variable, x, appearing on both sides of the equation. Below, the equation was the answer.

x = 0.217


I looked at the equation and then looked at the answer—repeatedly.

I don’t get frustrated with first-year chemistry too often, but this exercise was presenting a challenge and then to have the solution be nothing more than a single equation with no explanation left me exasperated.

Ten-steps later!

I have no idea why the publisher didn’t include a real solution, after all, it’s not like they need to conserve trees, but summarizing a complex problem to a single equation without additional context was less than helpful. For my eventual solution, each step documented the progression from what was known, to the unknown, and when completed, we understood the scope of the problem and how this problem fit into the section.

Sometimes, all we need is the answer—0.217. Sometimes, we need more—or we need to provide more. Were all ten steps required for this problem? Maybe not as some steps may have been self-evident, but for complex issues, I would prefer to receive too much information as opposed to too little.