Solving “Einstein's Riddle” Using Spreadsheet Optimization
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
A solution to Einstein's Riddle is presented using spreadsheet modelling and optimization. Various versions of this problem have been used in introductory management science (MS) classes either as an assignment or as a take-home exam. This riddle has proved to be a challenging problem, since it simultaneously integrates many of the elements that are taught throughout the semester. Namely, the ability to convert a somewhat complicated verbal description into requisite constraints, the creative modelling skills required to transform the problem into an assignment problem-type structure, no “true” or obvious objective function, a difficulty in determining what the (non-obvious) decision variables should be, the use of integer (binary) variables together with either-or constraints requiring satisfaction at equality (an added technical difficulty/challenge), the ubiquitous time issues involved in the solution of integer problems, the numerical representation of numbers by computers that are not readily obvious to business students (i.e. why supposedly integer values may appear in some form of scientific notation) and, most importantly, the ability to appropriately structure the problem formulation into a spreadsheet format for implementation with Solver.
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.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it