Problem: Password strength

Passwords are something about which almost everyone needs to be better informed. As part of a unit on combinatorics (or alternatively, as a unit on passwords in a tech class), students could look at passwords and how to make passwords more secure.

To get students thinking about password strength, this interactive password haystack calculator would be useful. Students could start by trying to make some secure passwords through the interactive calculator, and then they would probably have questions (like: Why is this password so much more secure than this other password?).

This list of the 25 most commonly used passwords is also useful to start some conversation on the difference between password haystack and password strength.

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Open-ended problem: Do groups of people follow predictable patterns?

My sister and I were walking our kids back from a trip to Science World, when we passed a park sparsely filled with people. My sister looked at the people sitting in the park, and wondered aloud, “I wonder if you can use mathematics to figure out how far apart people will sit on a lawn?” I looked carefully at the park too, and noticed that everyone seemed to be carefully at an maximal distance apart from anyone else on the field. I am particularly excited about my sister’s question, because she has always described herself as “not a math person.”

I decided to generalize her question, to “do groups of people follow predictable patterns?” This would allow for exploration in a wide variety of ways, for example:

  • Do people tend to follow the same paths when crossing open-space, like a field or in the meeting room of a train station?
  • How random is the motion of people as they sit waiting in a theatre?
  • Can you track use of phrases of language through groups of people?
  • What similarities exist, if any, between the networks of relationships each person has?