I disagree with this. I mean, I read it and felt mildly insulted, so higher than baseline chance I'm rationalizing, but
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:
The answer to "find the domain" is literal internet domains — the seven functions encode IP addresses that resolve to:
| # | IP Address | Domain |
|---|---|---|
| 1 | 72.163.4.185 | cisco.com |
| 2 | 140.82.116.3 | github.com |
| 3 | 138.1.33.162 | oracle.com |
| 4 | 157.240.229.35 | facebook.com (Meta) |
| 5 | 127.0.0.1 | localhost |
| 6 | 129.46.98.181 | qualcomm.com |
| 7 | 15.73.145.56 | hp.com |
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.
Each restricted function constrains the domain to an interval (or union of intervals) containing exactly one integer:
| # | Domain | Integer |
|---|---|---|
| 1 | (10/3 - sqrt(14)/6, 10/3 + sqrt(14)/6) ≈ (2.710, 3.957) | 3 |
| 2 | (4, 6) | 5 |
| 3 | ≈ [1.109, 2.224] | 2 |
| 4 | [-3/2, 3sin(-1)/2] ∪ (0, 3/2] | 1 |
| 5 | [≈0.434, ≈0.567] ∪ [≈7.933, ≈8.066] | 8 |
| 6 | (9/4 - sqrt(30)/8, 9/4 + sqrt(30)/8) ≈ (1.565, 2.935) | 2 |
| 7 | [2 - 4sqrt(17)/17, 2 + 4sqrt(17)/17] ≈ [1.030, 2.970] | 2 |
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 |
The (a)(b)(c)(d) tuples encode digit group sizes — how many digits each IP octet occupies:
| # | f(x) | Tuple | Split | IP |
|---|---|---|---|---|
| 1 | 721634185 | (2,3,1,3) | 72.163.4.185 | cisco.com |
| 2 | 140821163 | (3,2,3,1) | 140.82.116.3 | github.com |
| 3 | 138133162 | (3,1,2,3) | 138.1.33.162 | oracle.com |
| 4 | 15724022935 | (3,3,3,2) | 157.240.229.35 | facebook.com |
| 5 | 127001 | (3,1,1,1) | 127.0.0.1 | localhost |
| 6 | 1294698181 | (3,2,2,3) | 129.46.98.181 | qualcomm.com |
| 7 | 157314556 | (2,2,3,2) | 15.73.145.56 | hp.com |
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.
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 | 1 | f | |
| 5 | localhost | 8 | s |
| 6 | qualcomm | 2 | u |
| 7 | hp | 2 | p |
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.
Impossible Burger tastes fine to me, but — as Benjamin Franklin would say — it creates in the bowel a great quantity of wind, usually offensive to company.
I generally share your distaste for imitation meat, though. Tasty vegan or vegetarian food seems to come from cultures that have iterated on it for a while, and who don't seek to imitate meat-eating. Rastafari Ital is a pretty interesting historically-recent example.
I am not so sure about applying the general category of "slop". A sincere effort to figure out the features of X and replicate them without some undesired property Y, seems like a good thing to try. I am not sure it should be conflated with mechanical imitation.
Excerpt below, but read the (not much longer) full thing for the part involving Kolmogorov complexity. I suspect reading the full thing is better than reading the excerpt first for most people, in expectation. It's not that much longer.