99.7% Rejected in 84ms: Why I Stopped Making the Generator Smarter

I wrote a puzzle generator whose acceptance rate is 0.26% . It throws away 99.7% of everything it produces, and that is the design working as intended, not failing. Generating five valid puzzles takes 1,947 attempts and 84 milliseconds. The point is not the puzzles. The point is that the generator makes no correctness guarantee at all, and a verifier makes every one of them. Once you split those two responsibilities, "make the generator smarter" stops being the obvious optimisation — and that is exactly the position you are in when the generator is an LLM. The loop verigen is a Go CLI that produces cryptarithmetic puzzles — alphametics, the SEND + MORE = MONEY genre, where each letter stands for a distinct digit and the sum has to hold. The known answer to that one is 9567 + 1085 = 10652 . There is one rule, and everything else follows from it: The generator guarantees nothing. Every guarantee lives in the verifier. The generator throws plausible-looking letter combinations at the wall. The verifier does an exhaustive search and confirms two things: that a solution exists, and that it is unique. Anything that fails either check is discarded and the loop asks for another candidate. The loop itself knows nothing about cryptarithmetic. Implement a Domain interface and any other puzzle rides the same loop. What the log actually says Five puzzles, seed 7: ── Puzzle 2 [hard] HAIKU + BONSAI = KOKORO Answer: 96542 + 378165 = 474707 (attempts before this seed landed: 624) === generate/verify loop [alphametic] === seed=7 output=5 puzzles total attempts=1947 elapsed=84ms acceptance rate = 0.2568% (average 389 generations per puzzle) --- rejection reasons --- no unique solution 770 (39.55%) no solution 695 (35.70%) more than 10 distinct letters 477 (24.50%) ok 5 ( 0.26%) Nearly 40% of candidates have more than one valid solution. Another 36% have none. A quarter cannot possibly have one and are rejected before the search starts. Five survive. Filtering by difficulty makes it wo