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Simplex Lock Project Description Prerequisites Warm up Problems Hints Resources Teaching Notes Extension Problems Results
Simplex Lock
Simplex Lock graphic

You see here a lock made by the Simplex Company. They advertise "thousands of combinations." Are they telling the truth?

A combination is a sequence of 0-5 pushes. The pushes must follow these rules:

  • You can push any number of buttons, from 0 to 5
  • Once a button is pushed, it stays in (so it cannot be re-used in a later push).

Some possible combinations:

  • {1 2 3} {4 5} (push 1, 2, 3 together, then push 4 and 5 together)
  • {4 5} {1 2 3} (the order of pushes counts, but the order inside a push doesn’t)
  • {1}{3}{4, 5} (you don’t have to use every button)
  • {1 2 3 4 5} (push all the buttons at the same time)
  • {1} {3} {2} {5} {4} (using all five buttons in five pushes)
  • {} (no combination; the door is unlocked)

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