More than a trillion ways to mingle

Fifteen strangers walk into a bar, each determined to meet everyone else before the evening is over. How many different ways might they accomplish this?

All joking aside, there are 1,307,674,368,000 ways that any one individual could meet the other 14 strangers, without encountering anyone twice.

That’s the same calculation behind my catalog story, You Will All Be Punished Unless the Guilty Party Confesses. As I explain elsewhere on this site, this tale for teenagers exists in 15 episodes that can be read in any order. As with the meet-and-greet scenario, there are more than 1.3 trillion different ways of doing this, called permutations*. Despite the size of that answer, it’s the result of simple arithmetic. The calculation is: 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Four unique ways Mr. Pink could meet all 14 fellow party-goers. To show all 1,307,674,368,000 permutations would require making similar minimal changes one by one.

The figure to the right shows four of the huge number of unique ways that any of the 15 party-goers (such as Mr. Pink) could meet the other 14:

  1. a, b, c, d, e…
  2. a, c, b, d, e…
  3. a. c, d, b, e…
  4. a, c, d, e, b…

The figure also suggests similar unique variations in the way you could read 15 episodes of a story at random.

A spreadsheet program makes it easy to calculate permutations. Fortunately no math is necessary for real-life party-goers, or readers, and a mere 15 decisions is enough to eliminate the vast majority of possible choices.

* A mathematical permutation is an arrangement of objects (people, for example) in a specific order. In this case, no repetition is allowed within each set of 15 decisions because we assume that no two party guests meet more than once and no reader of You Will All Be Punished Unless the Guilty Party Confesses returns to an episode already read.

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