Bibliographic record
Abstract
Between 1962 and 1966 Claude Berge edited a series of columns that appeared in the Revue Française de Recherche Opérationnelle, entitled Problèmes plaisans et délectables, in homage of the 17th century work of Bachet. Each of these columns gives a new problem, along with solutions for earlier problems supplied by readers. The last of these columns contains a sorting problem, problem 41, in which we are given a string of n alternately white and black pegs on a one-dimensional board consisting of an unlimited number of empty holes. We are required to rearrange the pegs into a string of consecutive white and black pegs, using only moves which take a pair of adjacent pegs to two vacant adjacent holes. With h(n) denoting the minimum number of moves needed to obtain a string of white pegs followed by black pegs, Berge gives the values h(5) = 3, h(6) = 3 and h(7) = 4 and asks the reader to determine whether or not the function h(n) is increasing. This was the last issue of the Revue, and as far as we can tell, no solution has been published. In this note we offer a solution to problem 41 by showing that h(n) =⌈n/2 ⌉ for n�5.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.022 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.005 | 0.014 |
| Scholarly communication | 0.006 | 0.019 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.006 | 0.013 |
| Insufficient payload (model declined to judge) | 0.009 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".