Kinesys lands right in the middle of a village festival. From a stage shaped like a 3, a choir of Numerians is chanting a strange singsong, one number after another, each longer than the last.
Liz, who was just waiting for an excuse, launches into a low-gravity jig, flight suit and all. Dord covers his ears: “This makes no sense. No rule. It’s just noise.” M00N, on the other hand, sways to the beat and hums along: “I think there’s a rule, and a pretty one too!”
The choir stops abruptly, mid-verse. The conductor turns to the crew: whoever figures out how the song goes on gets to sing the next line.
The Riddle
What is the next term in this sequence?
1 – 11 – 21 – 1211 – 111221 – …
Hint
Don’t look for a math operation: in a way, each term describes what the previous one looks like.
Solution
The next term is 312211.
Each term comes from the previous one by “reading aloud” what’s written there: 1 is “one 1,” so 11; 11 is “two 1s,” so 21; 21 is “one 2, one 1,” so 1211; 1211 is “one 1, one 2, two 1s,” so 111221.
Finally, 111221 reads “three 1s, two 2s, one 1,” that is, 31 22 11: 312211.
The choir starts over, M00N sings the new line, and even Dord secretly taps his foot to the beat.