IBM Ponder This #331 · November 2025

We generate a sequence of strings $s_0,s_1,s_2,\dots$ in the following manner:

• $s_0$ = "CAT"
• $s_n$ is obtained from $s_{n-1}$ by substituting each letter of $s_{n-1}$ according to the following rules:

G -> T
T -> CA
C -> TG
A -> C

The first few steps yield the strings

CAT
TGCCA
CATTGTGC
TGCCACATCATTG

And so forth. One can see from the list that $s_3[3..7]$ is "CACA" (here $[a..b]$ means "all the letters, starting from the index $a$, up to and not including the index $b$, where indexing starts from 0")

Your goal: Find $s_n[n..(n+1000)]$ for $n={10}^{100}$

A bonus "*" will be given for finding $t_n[n..(n+1000)]$ for $n={10}^{100}$ where the sequence $t$ is defined simiarily to $s$ but with the initial value $t_0$ = "RABBITS" and the rules

G -> T,
T -> CA,
C -> BR,
A -> I,
R -> B,
B -> IS,
I -> TG,
S -> C,

Solution

Best opened after a real attempt

To be added.