Part One:
Two Was All They Knew
At some point you must have fallen asleep under the starlight. The fire has burned down to nothing but a cold ring of ash, and the guests from last night's story are gone. In their place, a group of men standing in deep concentration. They are dressed in lavish animal-skin robes and strange hats that almost resemble mortarboard caps with tassels. You get the strong feeling that these are scholars.
They chant as they arrange sticks and rocks on the ground. Watching them for a moment, you realize something curious: these primitive yet learned men possess an understanding of the numerical concepts of one and two, which they represent with sticks and rocks. As part of their process, they speak what they see (or they look and say…) describing the objects laid out before them exactly as they appear.
To explain their process, begin with a starting pattern of "1".
The first step is placing a single stick, representing 1.
The next step is to speak what is seen: one stick, or "one 1"… 11.
They lay two sticks now, corresponding to that utterance…
Observing the pattern, you follow the progression:
- 1 → one stick → "one 1" → 11
- 11 → two sticks → "two 1s" → 21
- 21 → one rock, one stick → "one 2, one 1"→ 1211
- 1211 → one stick, one rock, two sticks → "one 1, one 2, two 1s" → 111221
But, because these scholars lack the concept of three, things become strange. When they encounter 111, instead of saying "31", they break it apart:
- First "two sticks," then "one more stick". The result becomes 2111, or "two 1s and then one 1"
Their chanting flows effortlessly, even as the sequence grows longer and longer, each iteration stretching the line of sticks and rocks steadily farther across the dirt until they reach 65 iterations.
You feel the urge to join in.
One of the scholars notices and gives you a piece of parchment with a starting pattern of sticks and rocks, your puzzle input, for you to interpret and continue.
For example:
If your starting pattern is:
represented on the parchment as 121, the first 10 iterations would look like:
111211
21111221
1221212211
11221112112221
212221111221221211
121122122121221122111221
11122122112211121122212221112211
2111221122212221111221221211221221112221
1221112221221211221221212211221112212211222111221211
11222111221211221112212211221112112221222111221122212212211122111221
The length of the line after 10 iterations is 68.