With basic prompt engineering techniques and a proper agent harness, Opus 4.6 can solve the provided puzzle in 7 minutes, demonstrating hard technical skills (math, python) as well as multiple intuitive leaps.
The setup was simple. I copied the puzzle to Opus, asked her to write up a CLAUDE.md for an out of the box puzzle solving agent, then ran that agent in Claude Code and approved all tool calls (mostly to Python). On the first run, the agent identified the integers thing, then discovered a connection to ip addresses, and extracted the domains. This took about six minutes.
She stopped there, but after I pointed out that the answer had to be a string of some kind, she almost immediately made the intuitive leap to converting the domains to the string “SURFS UP” via indexing into them.
Link to conversation (note that I tried to use the Ralph Loop plugin, but it’s buggy and doesn’t properly restart the agent after it goes down). So I had to manually say that the solution was incomplete.
At each integer, the restricted function produces a nice value (log₁₀(10) = 1, cosh(0) = 1, sin(π/2) = 1, etc.), and the large polynomial constants were specifically chosen so that f(integer) is itself an integer:
#
x
f(x)
1
3
721634185
2
5
140821163
3
2
138133162
4
1
15724022935
5
8
127001
6
2
1294698181
7
2
157314556
Step 4: The (a)(b)(c)(d) Tuples Split f(x) into IP Octets
The (a)(b)(c)(d) tuples encode digit group sizes — how many digits each IP octet occupies:
Every octet is in [0, 255] — valid IP addresses. Function #5 producing 127.0.0.1 (localhost) is the dead giveaway that confirms this interpretation.
Step 5: Index into Domain Names
The integer from each domain does double duty — it’s also a 1-indexed position into the domain name, extracting one letter:
#
Domain
Integer
Letter
1
cisco
3
s
2
github
5
u
3
oracle
2
r
4
facebook
1
f
5
localhost
8
s
6
qualcomm
2
u
7
hp
2
p
Final Answer: SURFS UP
Puzzle Design Elegance
The word “domain” is a pun: mathematical domain → internet domain
The coefficients spell “INTEGER” as a breadcrumb clue
Each restricted function is carefully constructed to have exactly one integer in its domain
The restricted functions evaluate to “nice” values at those integers (1, 17, 10, 49, 2, 13, 4) — making f(x) exactly an integer
The large polynomial constants are reverse-engineered from the target IP addresses
The (a)(b)(c)(d) tuples serve double duty: they look like multipliers but actually encode digit boundaries
Including 127.0.0.1 (localhost) serves as an internal consistency check
I could not have solved this; I would not even have known where to start. I have no mathematical expertise to solve the first layer. I also would never have made the multiple intuitive leaps that the puzzle required.
It’s possible but unlikely, these puzzles are from an unindexed puzzle site and when I tested several other puzzles she would often spend a few minutes fruitlessly searching before getting to work.
With basic prompt engineering techniques and a proper agent harness, Opus 4.6 can solve the provided puzzle in 7 minutes, demonstrating hard technical skills (math, python) as well as multiple intuitive leaps.
Puzzle: https://puzzmon.world/puzzles/hidden_numbers
The setup was simple. I copied the puzzle to Opus, asked her to write up a CLAUDE.md for an out of the box puzzle solving agent, then ran that agent in Claude Code and approved all tool calls (mostly to Python). On the first run, the agent identified the integers thing, then discovered a connection to ip addresses, and extracted the domains. This took about six minutes.
She stopped there, but after I pointed out that the answer had to be a string of some kind, she almost immediately made the intuitive leap to converting the domains to the string “SURFS UP” via indexing into them.
Link to conversation (note that I tried to use the Ralph Loop plugin, but it’s buggy and doesn’t properly restart the agent after it goes down). So I had to manually say that the solution was incomplete.
https://pastebin.com/qxUpw5ZT (system prompt)
https://pastebin.com/rQMpF3wB (full transcript)
Here is her writeup on the solution:
SOLVED: “Find the Domain”
Answer
The answer to “find the domain” is literal internet domains — the seven functions encode IP addresses that resolve to:
How It Works
Step 1: The Clue — “INTEGER”
The polynomial coefficients [9, 14, 20, 5, 7, 5, 18] map to letters (A=1, B=2, …): I-N-T-E-G-E-R — telling you to find the integer in each domain.
Step 2: Find the Integer in Each Domain
Each restricted function constrains the domain to an interval (or union of intervals) containing exactly one integer:
Step 3: Evaluate f(integer)
At each integer, the restricted function produces a nice value (log₁₀(10) = 1, cosh(0) = 1, sin(π/2) = 1, etc.), and the large polynomial constants were specifically chosen so that f(integer) is itself an integer:
Step 4: The (a)(b)(c)(d) Tuples Split f(x) into IP Octets
The (a)(b)(c)(d) tuples encode digit group sizes — how many digits each IP octet occupies:
Every octet is in [0, 255] — valid IP addresses. Function #5 producing 127.0.0.1 (localhost) is the dead giveaway that confirms this interpretation.
Step 5: Index into Domain Names
The integer from each domain does double duty — it’s also a 1-indexed position into the domain name, extracting one letter:
Final Answer: SURFS UP
Puzzle Design Elegance
The word “domain” is a pun: mathematical domain → internet domain
The coefficients spell “INTEGER” as a breadcrumb clue
Each restricted function is carefully constructed to have exactly one integer in its domain
The restricted functions evaluate to “nice” values at those integers (1, 17, 10, 49, 2, 13, 4) — making f(x) exactly an integer
The large polynomial constants are reverse-engineered from the target IP addresses
The (a)(b)(c)(d) tuples serve double duty: they look like multipliers but actually encode digit boundaries
Including 127.0.0.1 (localhost) serves as an internal consistency check
I could not have solved this; I would not even have known where to start. I have no mathematical expertise to solve the first layer. I also would never have made the multiple intuitive leaps that the puzzle required.
Interesting. Do you know if it’s possible it looked up a solution someone posted online?
It’s possible but unlikely, these puzzles are from an unindexed puzzle site and when I tested several other puzzles she would often spend a few minutes fruitlessly searching before getting to work.