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The Josephus Problem: How math teaches us to solve problems

When I was in school, I always thought math word problems were a little funny. I understood that the point was for me to apply math to solve real-world problems, but the problems never felt real. However, these days I truly appreciate all of the ways that math taught me how to think about, break down, and work through problems.

Numberphile has a wonderful example of how to approach problem-solving with the Josephus problem:

These are the same skills you can use to solve a problem in support, as well:

  • Gather data about the problem
  • Look for patterns
  • Make a conjecture
  • Test your conjecture

As noted in the video, it’s also incredibly important to tackle small, discrete parts of the problem and work from there to the larger solution. If you stare at a big problem, it can look impossible to solve. But if you can prove theories about small parts of the problem, the larger solution can become clear.

Thank you to all of my teachers and others who encouraged me to learn and practice these skills — although I don’t do much pure math these days, I use these skills every day!

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