Don’t Always Trust Hints

Hints can sometimes distract you from better or faster ways of doing things

Keith McNulty

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I was recently tackling a math exam question for very able high school students. The question came with a hint on how to tackle it.

After some thought, it struck me that I had an easier way to tackle the problem if I ignored the hint. For a moment, I put myself in the shoes of a keen 18-year old who wants to do well in the exam. How many such students would be brave enough to ignore the hint and try their own approach? Probably not many.

It’s a good reminder that hints usually reflect one person’s way of attacking a problem, but that’s no guarantee that there aren’t alternative or even better ways to tackle it. Let’s take a look at the problem.

Sixth Term Examination Paper, Mathematics, 1991, Q4

Ignoring the hint

The hint tells us to focus on the area that the guard cannot see. But hold on. Let’s pretend we are the guard. As we walk back and forth from A to E, what can we see? Here is an alternative sketch of the diagram above:

I want to make a couple of simple observations:

  1. The guard can always…

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Keith McNulty

Pure and Applied Mathematician. LinkedIn Top Voice in Tech. Expert and Author in Data Science and Statistics. Find me on LinkedIn, Twitter or keithmcnulty.org