IBM Research | Ponder This | November 2025 Challenge

November2025 - Challenge

We generate a sequence of strings s_0, s_1, s_2, \ldots 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 similarly 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,

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

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Challenge: 28/10/2025 @ 16:00 PM EST
Solution: 05/12/2025 @ 12:00 AM EST
List Updated: 28/10/2025 @ 16:00 PM EST