From The Blacklistâ€¦

# Act 1

If you do know the four digits, how many combinationsÂ¹Â could there be?

# Act 2

Students mayÂ ask to see the four digits.

Remember to ask later if this information matters. That the digits are 1, 3, 4, 5 doesn’t; that there are four different digits — no repetition — does.

# Act 3

My hope is that this resolutionÂ feels sort of anticlimactic — thatÂ Raymond Reddington’s “Now there’s only twenty-four combinations” on the screen doesn’t measure up to students’Â shared strategies in the classroom.

Elizabeth Keen’s “Could be thousands of combinations” prior to Red’s sand trick could be an extension. At first viewing, it seems far-fetched that the character — an FBI profiler — doesn’t understand thatÂ there are exactly ten thousand four-digit possibilities (0000, 0001, 0002, â€¦, 9999). But has Liz assumed that the digits cannot repeat? If so, how many combinations could there be? Students can no longer answer this question by systematically listing and counting each possibility.

I imagine this task as an introduction to, not an application of, permutuations. ItÂ providesÂ a context for students to develop — not practice! — methods ofÂ counting without counting. Don’t bother if you’re anticipating a lot of knee-jerk 4!s from your students.

Â¹I know, I knowâ€¦ permutations.