FAILURE MAP
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FA-94796 / Exam timetabling constraints / Open access

Student at the daily limit reported · case 01

Students with exactly the allowed exams in a day are flagged.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The daily limit comparison is inclusive.

THE FAILURE

The daily limit comparison is inclusive.

Unsuccessful approach: Testing the student's total exam count flags every day they sit.

Case contract

sits [student, period] with spd periods per day (day = p // spd). Report ["day", student, day] when a student has more than maxday distinct periods on a day, and ["eve_morn", student, day] when a student sits the last period of a day and the first period of the next day. Rows by student: day findings by day, then evening-morning findings.

Why this case matters

Daily exam limits and evening-then-morning sequences are common student-welfare rules.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(sits, spd, maxday):
    by = {}
    for st, p in sits:
        by.setdefault(st, set()).add(p)
    out = []
    for st in sorted(by):
        ps = by[st]
        days = {}
        for p in ps:
            days[p // spd] = days.get(p // spd, 0) + 1
        for d in sorted(days):
            if days[d] >= maxday:
                out.append(['day', st, d])
        for p in sorted(ps):
            if p % spd == spd - 1 and p + 1 in ps:
                out.append(['eve_morn', st, p // spd])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: day limit boundary 1', [[['s1', 1], ['s1', 2]], 3, 2], []),
  ('regression variant: day limit boundary 2',
   [[['s2', 6], ['s3', 0], ['s2', 5], ['s2', 8], ['s3', 8], ['s1', 3]], 3, 1],
   [['day', 's2', 2], ['eve_morn', 's2', 1]]),
  ('partial repair guard 3', [[['s3', 4], ['s2', 8], ['s3', 1], ['s1', 1], ['s2', 3]], 3, 1], []),
  ('boundary control 4', [[['s1', 0], ['s1', 1], ['s1', 2]], 3, 2], [['day', 's1', 0]]),
  ('normal control 5', [[['s1', 4], ['s3', 4], ['s1', 6], ['s3', 6], ['s3', 2], ['s1', 1]], 3, 2], []),
  ('normal control 6', [[['s3', 3], ['s1', 0], ['s3', 0], ['s2', 4], ['s2', 2]], 2, 1], []),
  ('normal control 7', [[['s3', 10], ['s2', 5], ['s1', 0]], 4, 1], []),
  ('normal control 8', [[['s1', 11], ['s1', 5], ['s2', 10], ['s3', 3], ['s2', 0]], 4, 2], [])],
 [('regression: day limit boundary 1', [[['s1', 0], ['s1', 1]], 3, 2], []),
  ('regression variant: day limit boundary 2', [[['s1', 6], ['s3', 5], ['s3', 1], ['s3', 6]], 3, 1],
   [['eve_morn', 's3', 1]]),
  ('boundary control 3', [[['s1', 1], ['s1', 2]], 3, 2], []),
  ('normal control 4', [[['s3', 10], ['s2', 9]], 4, 2], []),
  ('normal control 5', [[['s3', 2], ['s2', 5], ['s1', 6], ['s3', 6], ['s1', 1]], 3, 1], []),
  ('normal control 6',
   [[['s3', 8], ['s2', 7], ['s1', 2], ['s3', 6], ['s2', 5], ['s2', 3], ['s2', 8], ['s2', 8]], 3, 1],
   [['day', 's2', 1], ['day', 's2', 2], ['day', 's3', 2]]),
  ('normal control 7',
   [[['s1', 2], ['s1', 6], ['s2', 2], ['s2', 5], ['s3', 0], ['s2', 5], ['s1', 7], ['s2', 4]], 4, 1],
   [['day', 's1', 1], ['day', 's2', 1]]),
  ('normal control 8',
   [[['s2', 4], ['s3', 0], ['s1', 1], ['s2', 3], ['s2', 2], ['s2', 4], ['s1', 5], ['s1', 0]], 2, 2],
   [['eve_morn', 's2', 1]])],
 [('regression: day limit boundary 1', [[['s3', 3], ['s1', 1], ['s2', 7], ['s3', 5], ['s3', 8]], 3, 1],
   [['day', 's3', 1]]),
  ('regression variant: day limit boundary 2',
   [[['s1', 1], ['s2', 6], ['s1', 4], ['s1', 3], ['s1', 4]], 3, 1], [['day', 's1', 1]]),
  ('partial repair guard 3', [[['s3', 6], ['s3', 8]], 4, 1], []),
  ('boundary control 4', [[['s1', 5], ['s1', 6]], 3, 2], [['eve_morn', 's1', 1]]),
  ('normal control 5', [[['s3', 1], ['s1', 4], ['s1', 3], ['s1', 8]], 3, 2], []),
  ('normal control 6', [[['s3', 1], ['s2', 5], ['s1', 2], ['s2', 2]], 2, 1], []),
  ('normal control 7', [[['s1', 4], ['s2', 4], ['s2', 4], ['s3', 5], ['s2', 1]], 4, 2], []),
  ('normal control 8', [[['s1', 1], ['s3', 2]], 4, 1], [])],
 [('regression: day limit boundary 1', [[['s2', 3], ['s3', 11], ['s1', 6], ['s3', 9]], 4, 2], []),
  ('regression variant: day limit boundary 2',
   [[['s1', 3], ['s3', 7], ['s3', 11], ['s3', 9], ['s2', 0], ['s1', 6], ['s3', 7], ['s1', 6]], 4, 2], []),
  ('partial repair guard 3', [[['s2', 0], ['s3', 4], ['s1', 2], ['s1', 5], ['s2', 4], ['s1', 0]], 2, 2], []),
  ('boundary control 4', [[['s1', 0], ['s1', 1]], 3, 2], []),
  ('normal control 5', [[['s1', 2], ['s1', 0], ['s1', 1], ['s1', 2], ['s3', 3], ['s3', 4], ['s3', 0]], 2, 2],
   [['eve_morn', 's1', 0], ['eve_morn', 's3', 1]]),
  ('normal control 6', [[['s2', 4], ['s3', 3]], 2, 2], []),
  ('normal control 7',
   [[['s2', 0], ['s3', 2], ['s1', 3], ['s2', 3], ['s2', 5], ['s3', 0], ['s1', 4], ['s3', 0]], 2, 2],
   [['eve_morn', 's1', 1]]),
  ('normal control 8', [[['s2', 0], ['s1', 3], ['s2', 4], ['s1', 5]], 2, 1], [])],
 [('regression: day limit boundary 1', [[['s3', 0], ['s3', 0], ['s1', 1], ['s3', 3], ['s1', 0]], 2, 2], []),
  ('regression variant: day limit boundary 2',
   [[['s2', 3], ['s1', 3], ['s3', 7], ['s3', 7], ['s3', 0]], 3, 1], []),
  ('partial repair guard 3',
   [[['s2', 0], ['s3', 0], ['s2', 7], ['s2', 5], ['s1', 0], ['s3', 1], ['s3', 6]], 3, 2], []),
  ('boundary control 4', [[['s1', 2], ['s1', 3]], 3, 2], [['eve_morn', 's1', 0]]),
  ('normal control 5', [[['s2', 2], ['s1', 2], ['s2', 5], ['s2', 5], ['s2', 8], ['s3', 5], ['s3', 2]], 3, 2],
   []),
  ('normal control 6', [[['s3', 1], ['s2', 3]], 2, 2], []),
  ('normal control 7',
   [[['s2', 5], ['s1', 5], ['s3', 5], ['s1', 3], ['s1', 1], ['s2', 4], ['s2', 2], ['s1', 2]], 2, 1],
   [['day', 's1', 1], ['eve_morn', 's1', 0], ['day', 's2', 2]]),
  ('normal control 8', [[['s1', 0], ['s1', 3], ['s2', 5], ['s1', 2]], 2, 1], [['day', 's1', 1]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: day limit boundary 1[['day', 's1', 0]][]Failed
regression variant: day limit boundary 2[['day', 's1', 1], ['day', 's2', 1], ['day', 's2', 2], ['eve_morn', 's2', 1], ['day', 's3', 0], ['day', 's3', 2]][['day', 's2', 2], ['eve_morn', 's2', 1]]Failed
partial repair guard 3[['day', 's1', 0], ['day', 's2', 1], ['day', 's2', 2], ['day', 's3', 0], ['day', 's3', 1]][]Failed
boundary control 4[['day', 's1', 0]][['day', 's1', 0]]Passed
normal control 5[][]Passed
normal control 6[['day', 's1', 0], ['day', 's2', 1], ['day', 's2', 2], ['day', 's3', 0], ['day', 's3', 1]][]Failed
normal control 7[['day', 's1', 0], ['day', 's2', 1], ['day', 's3', 2]][]Failed
normal control 8[][]Passed

SHA-256 / f0335654c28bfc0d77d6012f7854862341cb14a9c1159b1c3d1f366e9df80b87

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(sits, spd, maxday):
    by = {}
    for st, p in sits:
        by.setdefault(st, set()).add(p)
    out = []
    for st in sorted(by):
        ps = by[st]
        days = {}
        for p in ps:
            days[p // spd] = days.get(p // spd, 0) + 1
        for d in sorted(days):
            if len(ps) > maxday:
                out.append(['day', st, d])
        for p in sorted(ps):
            if p % spd == spd - 1 and p + 1 in ps:
                out.append(['eve_morn', st, p // spd])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: day limit boundary 1', [[['s1', 1], ['s1', 2]], 3, 2], []),
  ('regression variant: day limit boundary 2',
   [[['s2', 6], ['s3', 0], ['s2', 5], ['s2', 8], ['s3', 8], ['s1', 3]], 3, 1],
   [['day', 's2', 2], ['eve_morn', 's2', 1]]),
  ('partial repair guard 3', [[['s3', 4], ['s2', 8], ['s3', 1], ['s1', 1], ['s2', 3]], 3, 1], []),
  ('boundary control 4', [[['s1', 0], ['s1', 1], ['s1', 2]], 3, 2], [['day', 's1', 0]]),
  ('normal control 5', [[['s1', 4], ['s3', 4], ['s1', 6], ['s3', 6], ['s3', 2], ['s1', 1]], 3, 2], []),
  ('normal control 6', [[['s3', 3], ['s1', 0], ['s3', 0], ['s2', 4], ['s2', 2]], 2, 1], []),
  ('normal control 7', [[['s3', 10], ['s2', 5], ['s1', 0]], 4, 1], []),
  ('normal control 8', [[['s1', 11], ['s1', 5], ['s2', 10], ['s3', 3], ['s2', 0]], 4, 2], [])],
 [('regression: day limit boundary 1', [[['s1', 0], ['s1', 1]], 3, 2], []),
  ('regression variant: day limit boundary 2', [[['s1', 6], ['s3', 5], ['s3', 1], ['s3', 6]], 3, 1],
   [['eve_morn', 's3', 1]]),
  ('boundary control 3', [[['s1', 1], ['s1', 2]], 3, 2], []),
  ('normal control 4', [[['s3', 10], ['s2', 9]], 4, 2], []),
  ('normal control 5', [[['s3', 2], ['s2', 5], ['s1', 6], ['s3', 6], ['s1', 1]], 3, 1], []),
  ('normal control 6',
   [[['s3', 8], ['s2', 7], ['s1', 2], ['s3', 6], ['s2', 5], ['s2', 3], ['s2', 8], ['s2', 8]], 3, 1],
   [['day', 's2', 1], ['day', 's2', 2], ['day', 's3', 2]]),
  ('normal control 7',
   [[['s1', 2], ['s1', 6], ['s2', 2], ['s2', 5], ['s3', 0], ['s2', 5], ['s1', 7], ['s2', 4]], 4, 1],
   [['day', 's1', 1], ['day', 's2', 1]]),
  ('normal control 8',
   [[['s2', 4], ['s3', 0], ['s1', 1], ['s2', 3], ['s2', 2], ['s2', 4], ['s1', 5], ['s1', 0]], 2, 2],
   [['eve_morn', 's2', 1]])],
 [('regression: day limit boundary 1', [[['s3', 3], ['s1', 1], ['s2', 7], ['s3', 5], ['s3', 8]], 3, 1],
   [['day', 's3', 1]]),
  ('regression variant: day limit boundary 2',
   [[['s1', 1], ['s2', 6], ['s1', 4], ['s1', 3], ['s1', 4]], 3, 1], [['day', 's1', 1]]),
  ('partial repair guard 3', [[['s3', 6], ['s3', 8]], 4, 1], []),
  ('boundary control 4', [[['s1', 5], ['s1', 6]], 3, 2], [['eve_morn', 's1', 1]]),
  ('normal control 5', [[['s3', 1], ['s1', 4], ['s1', 3], ['s1', 8]], 3, 2], []),
  ('normal control 6', [[['s3', 1], ['s2', 5], ['s1', 2], ['s2', 2]], 2, 1], []),
  ('normal control 7', [[['s1', 4], ['s2', 4], ['s2', 4], ['s3', 5], ['s2', 1]], 4, 2], []),
  ('normal control 8', [[['s1', 1], ['s3', 2]], 4, 1], [])],
 [('regression: day limit boundary 1', [[['s2', 3], ['s3', 11], ['s1', 6], ['s3', 9]], 4, 2], []),
  ('regression variant: day limit boundary 2',
   [[['s1', 3], ['s3', 7], ['s3', 11], ['s3', 9], ['s2', 0], ['s1', 6], ['s3', 7], ['s1', 6]], 4, 2], []),
  ('partial repair guard 3', [[['s2', 0], ['s3', 4], ['s1', 2], ['s1', 5], ['s2', 4], ['s1', 0]], 2, 2], []),
  ('boundary control 4', [[['s1', 0], ['s1', 1]], 3, 2], []),
  ('normal control 5', [[['s1', 2], ['s1', 0], ['s1', 1], ['s1', 2], ['s3', 3], ['s3', 4], ['s3', 0]], 2, 2],
   [['eve_morn', 's1', 0], ['eve_morn', 's3', 1]]),
  ('normal control 6', [[['s2', 4], ['s3', 3]], 2, 2], []),
  ('normal control 7',
   [[['s2', 0], ['s3', 2], ['s1', 3], ['s2', 3], ['s2', 5], ['s3', 0], ['s1', 4], ['s3', 0]], 2, 2],
   [['eve_morn', 's1', 1]]),
  ('normal control 8', [[['s2', 0], ['s1', 3], ['s2', 4], ['s1', 5]], 2, 1], [])],
 [('regression: day limit boundary 1', [[['s3', 0], ['s3', 0], ['s1', 1], ['s3', 3], ['s1', 0]], 2, 2], []),
  ('regression variant: day limit boundary 2',
   [[['s2', 3], ['s1', 3], ['s3', 7], ['s3', 7], ['s3', 0]], 3, 1], []),
  ('partial repair guard 3',
   [[['s2', 0], ['s3', 0], ['s2', 7], ['s2', 5], ['s1', 0], ['s3', 1], ['s3', 6]], 3, 2], []),
  ('boundary control 4', [[['s1', 2], ['s1', 3]], 3, 2], [['eve_morn', 's1', 0]]),
  ('normal control 5', [[['s2', 2], ['s1', 2], ['s2', 5], ['s2', 5], ['s2', 8], ['s3', 5], ['s3', 2]], 3, 2],
   []),
  ('normal control 6', [[['s3', 1], ['s2', 3]], 2, 2], []),
  ('normal control 7',
   [[['s2', 5], ['s1', 5], ['s3', 5], ['s1', 3], ['s1', 1], ['s2', 4], ['s2', 2], ['s1', 2]], 2, 1],
   [['day', 's1', 1], ['eve_morn', 's1', 0], ['day', 's2', 2]]),
  ('normal control 8', [[['s1', 0], ['s1', 3], ['s2', 5], ['s1', 2]], 2, 1], [['day', 's1', 1]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: day limit boundary 1[][]Passed
regression variant: day limit boundary 2[['day', 's2', 1], ['day', 's2', 2], ['eve_morn', 's2', 1], ['day', 's3', 0], ['day', 's3', 2]][['day', 's2', 2], ['eve_morn', 's2', 1]]Failed
partial repair guard 3[['day', 's2', 1], ['day', 's2', 2], ['day', 's3', 0], ['day', 's3', 1]][]Failed
boundary control 4[['day', 's1', 0]][['day', 's1', 0]]Passed
normal control 5[['day', 's1', 0], ['day', 's1', 1], ['day', 's1', 2], ['day', 's3', 0], ['day', 's3', 1], ['day', 's3', 2]][]Failed
normal control 6[['day', 's2', 1], ['day', 's2', 2], ['day', 's3', 0], ['day', 's3', 1]][]Failed
normal control 7[][]Passed
normal control 8[][]Passed

SHA-256 / 75954e95b15746f3dd02daca8e814d94fd63db281be9d59dfef48376304b5662

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

Stipulated toy exam-timetabling rule set for a bounded model; it does not claim conformance with any institution's regulations or a benchmark specification, and it performs no search or optimisation. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:52:07.788851+00:00.

Case digest / 8bff95a1e615ca8ab35e5bde36830f8188be1385bc3c977759e5d90c1f22955b