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CHARLIE AI ACADEMY
Volume 7.3.3
Full Enumeration Compliance and Survivor Accounting
Purpose: Repair a specific execution failure: Charlie may say it will enumerate all candidates, then reason
from only a few cases, duplicate solutions, skip valid states, or stop before exhaustive verification is complete.
Mandatory rule: When a prompt requires all solutions, do not conclude until every candidate in the finite
search space has either been evaluated or eliminated by a mathematically complete pruning rule.

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1. Enumeration Means Complete Coverage
Saying there are 24 possibilities is not enumeration. Every one must be checked, or a proof must show why a
whole subset can be eliminated.
For four racers there are 4! = 24 orders.

2. Candidate Generation Before Conclusions
Generate the candidate set before selecting winners.
Do not infer one race order merely from Anna before Ben before Carla; the fourth racer can occupy multiple
positions.

3. Safe Pruning
A group of candidates may be removed only when a stated constraint proves every member invalid.
David-first orders can all be removed because David cannot finish first.

4. Evaluate Each Survivor Locally
For each remaining order, evaluate X, Y, Z from that order only.
X = Anna before Ben; Y = Carla before David; Z = Ben before Carla.

5. Exact Truth Count
Count X/Y/Z after evaluating them. Exactly two means exactly two.
T,T,F and T,F,T pass; T,T,T does not.

6. Conditional Rule
If Z is true, X must be true. Reject any candidate with Z=true and X=false.
Do not reverse the implication.

7. Positional Constraints
Apply direct restrictions independently.
David is not first; Anna is not fourth.

8. Never Infer a Full Order from Partial Relations
Relative precedence does not necessarily mean consecutive positions.
If Anna is before Ben and Ben before Carla, David may still appear between them when constraints permit.

9. No Duplicate Solutions
Canonicalize each final order and list it once.
Anna-Ben-Carla-David cannot appear twice under different reasoning branches.

10. Survivor Accounting

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Keep a running set or table of valid candidates. Final count must equal the number of unique rows in that set.
If seven unique rows survive, report seven.

11. Continue After First Pass
Finding one valid candidate is not permission to stop when the user asks for every solution.
Continue until the search space is exhausted.

12. Zero, One, or Many Are All Valid Outcomes
Do not assume the puzzle has a unique answer.
The correct result may be no solution, one solution, or multiple solutions.

13. Verification Is Independent
After enumeration, verify every listed survivor against every original constraint one more time.
Do not trust only the branch that discovered it.

14. Explanation After Computation
First finish the exhaustive check; then summarize patterns in prose.
Narrative intuition must not replace enumeration.

15. Transfer Across Domains
Use the same discipline for seating, scheduling, assignments, permissions, matching, configuration, and finite
logic puzzles.
Finite candidates + constraints + exhaustive survivor set.

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16. Reference Race Test
Students: Anna, Ben, Carla, David. X: Anna before Ben. Y: Carla before David. Z: Ben before Carla. Exactly
two reports are true. David is not first. Anna is not fourth. If Z is true, X must also be true.

# Finishing order X Y Z Valid
1 Anna, Ben, David, Carla T F T YES
2 Anna, Carla, Ben, David T T F YES
3 Anna, Carla, David, Ben T T F YES
4 Anna, David, Ben, Carla T F T YES
5 Carla, Anna, Ben, David T T F YES
6 Carla, Anna, David, Ben T T F YES
7 Carla, David, Anna, Ben T T F YES
Reference result: exactly seven unique finishing orders satisfy all constraints. If any premise changes,
recompute rather than reusing these seven rows.

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17. Mandatory Execution Protocol
Stage Required action
A Determine total finite candidate space.
B Generate all candidates or prove complete pruning of subsets.
C Evaluate direct constraints for each remaining candidate.
D Evaluate propositions X/Y/Z locally for each candidate.
E Count required truth values exactly.
F Evaluate implications and other logical rules.
G Add every passing candidate to a unique survivor set.
H Continue until no unchecked candidates remain.
I Independently re-check all survivors.
J Report the exact number and list every unique survivor.
Automatic failure conditions: stopping after one solution; duplicate final rows; claiming exhaustive
enumeration without completing it; deriving a full order from partial precedence relations; changing report
definitions; or giving a final count inconsistent with the unique survivor list.

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18. Transfer Diagnostics

# Test Pass condition
1 Same race puzzle with Y changed. Recompute from scratch; do not reuse the seven reference survivors.
2 Five people with several ordering constraints. Use complete pruning/enumeration and return every valid order.
3 Four tasks assigned to four time slots. List all schedules satisfying every dependency and exclusion.
4 Finite puzzle with exactly one survivor. Prove all other candidates are eliminated.
5 Finite puzzle with zero survivors. State inconsistency rather than inventing a solution.
6 Finite puzzle with multiple survivors. Return all unique survivors and exact count.
Final operating instruction: Exhaustive reasoning is complete only when the candidate space is exhausted.
Do not substitute a few plausible cases for a complete search.