FA-94416 / Exam timetabling constraints / Open access

Proximity weight grows with distance · case 01

Exams far apart are penalised more than adjacent ones.

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

ROOT CAUSE

The weight exponent is reversed.

THE FAILURE

The weight exponent is reversed.

Unsuccessful approach: An inverse-distance weight does not match the halving schedule.

Case contract

enrol [student, exam] rows (may repeat) and exam periods. For each student, each pair of distinct exams d = 1..5 periods apart costs 2^(5-d). Return [total, number of students, total/students as a reduced fraction string].

Why this case matters

The Carter proximity cost is the standard exam-timetabling quality measure; each piece has a known implementation pitfall.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(enrol, period):
    by = {}
    for st, ex in enrol:
        by.setdefault(st, set()).add(ex)
    total = 0
    for st, exs in by.items():
        ps = sorted(period[e] for e in exs)
        for i in range(len(ps)):
            for j in range(i + 1, len(ps)):
                d = ps[j] - ps[i]
                if 1 <= d <= 5:
                    total += 2 ** (d - 1)
    n = len(by)
    return [total, n, str(Fraction(total, n)) if n else '0']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: proximity weight 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('regression variant: proximity weight 2',
   [[['s2', 'HIST140'], ['s2', 'BIO130'], ['s2', 'CHEM120'], ['s1', 'ECON150'], ['s1', 'MATH101H'],
     ['s2', 'PHYS110'], ['s1', 'MATH101'], ['s3', 'MATH101'], ['s1', 'ECON150'], ['s4', 'MATH101H'],
     ['s4', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 6, 'PHYS110': 3, 'CHEM120': 4, 'BIO130': 4, 'HIST140': 4, 'ECON150': 0}],
   [52, 4, '13']),
  ('partial repair guard 3',
   [[['s4', 'HIST140'], ['s5', 'MATH101H'], ['s2', 'CHEM120'], ['s1', 'BIO130'], ['s1', 'MATH101H'],
     ['s4', 'MATH101'], ['s4', 'PHYS110'], ['s1', 'CHEM120'], ['s4', 'ECON150'], ['s5', 'ECON150'],
     ['s1', 'HIST140'], ['s1', 'BIO130'], ['s5', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 0, 'PHYS110': 0, 'CHEM120': 2, 'BIO130': 5, 'HIST140': 1, 'ECON150': 5}],
   [105, 4, '105/4']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s1', 'BIO130'], ['s1', 'HIST140'], ['s1', 'PHYS110'], ['s3', 'ECON150'], ['s3', 'PHYS110'],
     ['s4', 'HIST140'], ['s3', 'HIST140'], ['s3', 'BIO130'], ['s1', 'CHEM120']],
    {'MATH101': 4, 'MATH101H': 3, 'PHYS110': 3, 'CHEM120': 2, 'BIO130': 4, 'HIST140': 7, 'ECON150': 0}],
   [75, 3, '25']),
  ('normal control 7',
   [[['s1', 'PHYS110'], ['s5', 'CHEM120'], ['s5', 'HIST140'], ['s4', 'BIO130'], ['s5', 'MATH101'],
     ['s1', 'HIST140'], ['s4', 'CHEM120'], ['s2', 'MATH101H'], ['s2', 'CHEM120'], ['s1', 'CHEM120']],
    {'MATH101': 7, 'MATH101H': 7, 'PHYS110': 2, 'CHEM120': 5, 'BIO130': 4, 'HIST140': 4, 'ECON150': 4}],
   [80, 4, '20']),
  ('normal control 8',
   [[['s5', 'PHYS110'], ['s2', 'PHYS110'], ['s2', 'CHEM120'], ['s1', 'CHEM120'], ['s1', 'PHYS110'],
     ['s5', 'ECON150'], ['s3', 'HIST140'], ['s2', 'ECON150'], ['s1', 'HIST140'], ['s2', 'MATH101H'],
     ['s4', 'HIST140'], ['s4', 'MATH101H'], ['s3', 'PHYS110']],
    {'MATH101': 3, 'MATH101H': 4, 'PHYS110': 7, 'CHEM120': 7, 'BIO130': 7, 'HIST140': 0, 'ECON150': 7}],
   [14, 5, '14/5'])],
 [('regression: proximity weight 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 5}],
   [1, 1, '1']),
  ('regression variant: proximity weight 2',
   [[['s2', 'HIST140'], ['s2', 'BIO130'], ['s3', 'ECON150'], ['s3', 'MATH101H'], ['s3', 'CHEM120'],
     ['s4', 'HIST140'], ['s2', 'PHYS110'], ['s3', 'BIO130']],
    {'MATH101': 3, 'MATH101H': 6, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 5, 'HIST140': 6, 'ECON150': 6}],
   [76, 3, '76/3']),
  ('partial repair guard 3',
   [[['s2', 'PHYS110'], ['s2', 'MATH101H']],
    {'MATH101': 2, 'MATH101H': 4, 'PHYS110': 1, 'CHEM120': 4, 'BIO130': 5, 'HIST140': 3, 'ECON150': 3}],
   [4, 1, '4']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('boundary control 5',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('normal control 6',
   [[['s1', 'CHEM120'], ['s2', 'CHEM120'], ['s2', 'ECON150'], ['s1', 'ECON150'], ['s1', 'MATH101'],
     ['s1', 'CHEM120'], ['s2', 'HIST140'], ['s2', 'BIO130']],
    {'MATH101': 7, 'MATH101H': 4, 'PHYS110': 1, 'CHEM120': 4, 'BIO130': 3, 'HIST140': 5, 'ECON150': 7}],
   [62, 2, '31']),
  ('normal control 7',
   [[['s4', 'CHEM120'], ['s4', 'PHYS110'], ['s5', 'MATH101H'], ['s2', 'CHEM120'], ['s4', 'MATH101'],
     ['s5', 'HIST140'], ['s2', 'ECON150'], ['s2', 'MATH101H'], ['s5', 'CHEM120']],
    {'MATH101': 3, 'MATH101H': 1, 'PHYS110': 1, 'CHEM120': 6, 'BIO130': 7, 'HIST140': 6, 'ECON150': 6}],
   [17, 3, '17/3']),
  ('normal control 8',
   [[['s2', 'PHYS110'], ['s2', 'ECON150']],
    {'MATH101': 6, 'MATH101H': 1, 'PHYS110': 2, 'CHEM120': 2, 'BIO130': 5, 'HIST140': 3, 'ECON150': 1}],
   [16, 1, '16'])],
 [('regression: proximity weight 1',
   [[['s1', 'MATH101'], ['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 2}], [8, 1, '8']),
  ('regression variant: proximity weight 2',
   [[['s5', 'PHYS110'], ['s5', 'BIO130'], ['s4', 'ECON150'], ['s5', 'HIST140'], ['s5', 'PHYS110'],
     ['s5', 'MATH101H'], ['s1', 'CHEM120'], ['s1', 'ECON150'], ['s4', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 4, 'PHYS110': 2, 'CHEM120': 5, 'BIO130': 5, 'HIST140': 3, 'ECON150': 1}],
   [78, 3, '26']),
  ('partial repair guard 3',
   [[['s4', 'ECON150'], ['s4', 'MATH101H'], ['s3', 'MATH101H'], ['s4', 'HIST140'], ['s1', 'PHYS110'],
     ['s4', 'PHYS110'], ['s1', 'BIO130'], ['s1', 'MATH101'], ['s1', 'CHEM120']],
    {'MATH101': 3, 'MATH101H': 7, 'PHYS110': 7, 'CHEM120': 4, 'BIO130': 0, 'HIST140': 7, 'ECON150': 1}],
   [28, 3, '28/3']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s3', 'CHEM120'], ['s4', 'BIO130'], ['s4', 'PHYS110'], ['s3', 'ECON150'], ['s2', 'MATH101'],
     ['s4', 'MATH101H'], ['s3', 'PHYS110']],
    {'MATH101': 3, 'MATH101H': 6, 'PHYS110': 5, 'CHEM120': 3, 'BIO130': 4, 'HIST140': 5, 'ECON150': 7}],
   [58, 3, '58/3']),
  ('normal control 7',
   [[['s3', 'BIO130'], ['s2', 'ECON150'], ['s1', 'ECON150'], ['s3', 'MATH101H'], ['s3', 'PHYS110'],
     ['s2', 'MATH101H'], ['s1', 'CHEM120'], ['s5', 'HIST140']],
    {'MATH101': 2, 'MATH101H': 1, 'PHYS110': 7, 'CHEM120': 0, 'BIO130': 1, 'HIST140': 5, 'ECON150': 1}],
   [16, 4, '4']),
  ('normal control 8',
   [[['s2', 'BIO130'], ['s2', 'HIST140'], ['s2', 'MATH101'], ['s2', 'PHYS110'], ['s5', 'HIST140'],
     ['s3', 'CHEM120'], ['s5', 'ECON150'], ['s3', 'MATH101H'], ['s5', 'MATH101'], ['s5', 'MATH101H'],
     ['s2', 'HIST140']],
    {'MATH101': 1, 'MATH101H': 4, 'PHYS110': 7, 'CHEM120': 2, 'BIO130': 4, 'HIST140': 1, 'ECON150': 6}],
   [38, 3, '38/3'])],
 [('regression: proximity weight 1',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('regression variant: proximity weight 2',
   [[['s4', 'MATH101H'], ['s5', 'MATH101'], ['s5', 'HIST140'], ['s1', 'MATH101H'], ['s1', 'ECON150'],
     ['s1', 'PHYS110'], ['s5', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'PHYS110'], ['s1', 'HIST140'],
     ['s3', 'PHYS110'], ['s5', 'MATH101'], ['s2', 'HIST140'], ['s2', 'BIO130'], ['s4', 'MATH101']],
    {'MATH101': 0, 'MATH101H': 0, 'PHYS110': 5, 'CHEM120': 2, 'BIO130': 3, 'HIST140': 6, 'ECON150': 7}],
   [94, 5, '94/5']),
  ('partial repair guard 3',
   [[['s5', 'CHEM120'], ['s3', 'MATH101H'], ['s2', 'ECON150'], ['s5', 'MATH101H'], ['s1', 'ECON150'],
     ['s4', 'CHEM120'], ['s2', 'CHEM120'], ['s3', 'BIO130'], ['s4', 'PHYS110'], ['s5', 'ECON150'],
     ['s3', 'ECON150'], ['s2', 'PHYS110'], ['s5', 'HIST140'], ['s4', 'MATH101H'], ['s4', 'BIO130'],
     ['s4', 'BIO130'], ['s3', 'HIST140'], ['s2', 'MATH101H']],
    {'MATH101': 3, 'MATH101H': 6, 'PHYS110': 1, 'CHEM120': 1, 'BIO130': 6, 'HIST140': 6, 'ECON150': 5}],
   [110, 5, '22']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('normal control 5',
   [[['s5', 'MATH101'], ['s3', 'BIO130'], ['s5', 'CHEM120'], ['s2', 'ECON150'], ['s2', 'PHYS110'],
     ['s2', 'PHYS110'], ['s2', 'MATH101H']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 6, 'HIST140': 7, 'ECON150': 6}],
   [11, 3, '11/3']),
  ('normal control 6',
   [[['s2', 'HIST140'], ['s2', 'BIO130'], ['s3', 'ECON150'], ['s3', 'MATH101H'], ['s3', 'CHEM120'],
     ['s4', 'HIST140'], ['s2', 'PHYS110'], ['s3', 'BIO130']],
    {'MATH101': 3, 'MATH101H': 6, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 5, 'HIST140': 6, 'ECON150': 6}],
   [76, 3, '76/3']),
  ('normal control 7',
   [[['s5', 'MATH101'], ['s5', 'HIST140'], ['s1', 'HIST140'], ['s1', 'BIO130'], ['s5', 'BIO130'],
     ['s1', 'PHYS110'], ['s2', 'HIST140']],
    {'MATH101': 4, 'MATH101H': 7, 'PHYS110': 7, 'CHEM120': 6, 'BIO130': 3, 'HIST140': 2, 'ECON150': 4}],
   [59, 3, '59/3']),
  ('normal control 8',
   [[['s1', 'MATH101H'], ['s1', 'CHEM120'], ['s3', 'HIST140'], ['s3', 'PHYS110'], ['s3', 'MATH101'],
     ['s3', 'ECON150'], ['s4', 'PHYS110'], ['s3', 'HIST140']],
    {'MATH101': 4, 'MATH101H': 4, 'PHYS110': 6, 'CHEM120': 7, 'BIO130': 0, 'HIST140': 0, 'ECON150': 5}],
   [47, 3, '47/3'])],
 [('regression: proximity weight 1',
   [[['s3', 'CHEM120'], ['s1', 'MATH101'], ['s2', 'CHEM120'], ['s5', 'HIST140'], ['s5', 'BIO130'],
     ['s1', 'HIST140'], ['s1', 'CHEM120'], ['s1', 'BIO130'], ['s3', 'BIO130'], ['s2', 'MATH101H'],
     ['s2', 'MATH101'], ['s2', 'HIST140']],
    {'MATH101': 2, 'MATH101H': 0, 'PHYS110': 3, 'CHEM120': 5, 'BIO130': 4, 'HIST140': 0, 'ECON150': 0}],
   [79, 4, '79/4']),
  ('regression variant: proximity weight 2',
   [[['s5', 'MATH101H'], ['s3', 'HIST140'], ['s4', 'ECON150'], ['s5', 'CHEM120'], ['s4', 'HIST140'],
     ['s5', 'HIST140'], ['s3', 'ECON150'], ['s4', 'ECON150'], ['s3', 'MATH101']],
    {'MATH101': 2, 'MATH101H': 4, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 1, 'HIST140': 1, 'ECON150': 3}],
   [76, 3, '76/3']),
  ('partial repair guard 3',
   [[['s5', 'PHYS110'], ['s5', 'BIO130'], ['s4', 'ECON150'], ['s5', 'HIST140'], ['s5', 'PHYS110'],
     ['s5', 'MATH101H'], ['s1', 'CHEM120'], ['s1', 'ECON150'], ['s4', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 4, 'PHYS110': 2, 'CHEM120': 5, 'BIO130': 5, 'HIST140': 3, 'ECON150': 1}],
   [78, 3, '26']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s2', 'ECON150'], ['s2', 'ECON150'], ['s4', 'MATH101H'], ['s4', 'HIST140'], ['s3', 'HIST140'],
     ['s3', 'PHYS110'], ['s3', 'CHEM120'], ['s3', 'MATH101'], ['s2', 'PHYS110'], ['s4', 'CHEM120'],
     ['s4', 'BIO130'], ['s2', 'CHEM120'], ['s1', 'MATH101']],
    {'MATH101': 7, 'MATH101H': 5, 'PHYS110': 3, 'CHEM120': 2, 'BIO130': 7, 'HIST140': 4, 'ECON150': 5}],
   [116, 4, '29']),
  ('normal control 7',
   [[['s2', 'BIO130'], ['s3', 'ECON150'], ['s4', 'BIO130'], ['s2', 'MATH101H'], ['s1', 'BIO130'],
     ['s1', 'MATH101'], ['s5', 'HIST140'], ['s2', 'MATH101H'], ['s2', 'MATH101'], ['s1', 'PHYS110'],
     ['s4', 'CHEM120'], ['s2', 'ECON150'], ['s1', 'MATH101H']],
    {'MATH101': 6, 'MATH101H': 2, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 4, 'HIST140': 4, 'ECON150': 4}],
   [77, 5, '77/5']),
  ('normal control 8',
   [[['s2', 'PHYS110'], ['s1', 'PHYS110'], ['s2', 'CHEM120'], ['s2', 'ECON150'], ['s1', 'CHEM120'],
     ['s5', 'BIO130'], ['s5', 'ECON150'], ['s1', 'ECON150'], ['s1', 'HIST140'], ['s2', 'BIO130']],
    {'MATH101': 3, 'MATH101H': 5, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 2, 'HIST140': 6, 'ECON150': 1}],
   [67, 3, '67/3'])]]
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 fixture	Actual	Expected	Outcome
regression: proximity weight 1	`[1, 1, '1']`	`[16, 1, '16']`	Failed
regression variant: proximity weight 2	`[7, 4, '7/4']`	`[52, 4, '13']`	Failed
partial repair guard 3	`[90, 4, '45/2']`	`[105, 4, '105/4']`	Failed
boundary control 4	`[0, 1, '0']`	`[0, 1, '0']`	Passed
boundary control 5	`[0, 1, '0']`	`[0, 1, '0']`	Passed
normal control 6	`[57, 3, '19']`	`[75, 3, '25']`	Failed
normal control 7	`[17, 4, '17/4']`	`[80, 4, '20']`	Failed
normal control 8	`[20, 5, '4']`	`[14, 5, '14/5']`	Failed

SHA-256 / 6ab15dd54b1ee93452b9c7c16183cd78c8047ff0a164878e2807cd14ba1f3121

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(enrol, period):
    by = {}
    for st, ex in enrol:
        by.setdefault(st, set()).add(ex)
    total = 0
    for st, exs in by.items():
        ps = sorted(period[e] for e in exs)
        for i in range(len(ps)):
            for j in range(i + 1, len(ps)):
                d = ps[j] - ps[i]
                if 1 <= d <= 5:
                    total += 32 // d
    n = len(by)
    return [total, n, str(Fraction(total, n)) if n else '0']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: proximity weight 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('regression variant: proximity weight 2',
   [[['s2', 'HIST140'], ['s2', 'BIO130'], ['s2', 'CHEM120'], ['s1', 'ECON150'], ['s1', 'MATH101H'],
     ['s2', 'PHYS110'], ['s1', 'MATH101'], ['s3', 'MATH101'], ['s1', 'ECON150'], ['s4', 'MATH101H'],
     ['s4', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 6, 'PHYS110': 3, 'CHEM120': 4, 'BIO130': 4, 'HIST140': 4, 'ECON150': 0}],
   [52, 4, '13']),
  ('partial repair guard 3',
   [[['s4', 'HIST140'], ['s5', 'MATH101H'], ['s2', 'CHEM120'], ['s1', 'BIO130'], ['s1', 'MATH101H'],
     ['s4', 'MATH101'], ['s4', 'PHYS110'], ['s1', 'CHEM120'], ['s4', 'ECON150'], ['s5', 'ECON150'],
     ['s1', 'HIST140'], ['s1', 'BIO130'], ['s5', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 0, 'PHYS110': 0, 'CHEM120': 2, 'BIO130': 5, 'HIST140': 1, 'ECON150': 5}],
   [105, 4, '105/4']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s1', 'BIO130'], ['s1', 'HIST140'], ['s1', 'PHYS110'], ['s3', 'ECON150'], ['s3', 'PHYS110'],
     ['s4', 'HIST140'], ['s3', 'HIST140'], ['s3', 'BIO130'], ['s1', 'CHEM120']],
    {'MATH101': 4, 'MATH101H': 3, 'PHYS110': 3, 'CHEM120': 2, 'BIO130': 4, 'HIST140': 7, 'ECON150': 0}],
   [75, 3, '25']),
  ('normal control 7',
   [[['s1', 'PHYS110'], ['s5', 'CHEM120'], ['s5', 'HIST140'], ['s4', 'BIO130'], ['s5', 'MATH101'],
     ['s1', 'HIST140'], ['s4', 'CHEM120'], ['s2', 'MATH101H'], ['s2', 'CHEM120'], ['s1', 'CHEM120']],
    {'MATH101': 7, 'MATH101H': 7, 'PHYS110': 2, 'CHEM120': 5, 'BIO130': 4, 'HIST140': 4, 'ECON150': 4}],
   [80, 4, '20']),
  ('normal control 8',
   [[['s5', 'PHYS110'], ['s2', 'PHYS110'], ['s2', 'CHEM120'], ['s1', 'CHEM120'], ['s1', 'PHYS110'],
     ['s5', 'ECON150'], ['s3', 'HIST140'], ['s2', 'ECON150'], ['s1', 'HIST140'], ['s2', 'MATH101H'],
     ['s4', 'HIST140'], ['s4', 'MATH101H'], ['s3', 'PHYS110']],
    {'MATH101': 3, 'MATH101H': 4, 'PHYS110': 7, 'CHEM120': 7, 'BIO130': 7, 'HIST140': 0, 'ECON150': 7}],
   [14, 5, '14/5'])],
 [('regression: proximity weight 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 5}],
   [1, 1, '1']),
  ('regression variant: proximity weight 2',
   [[['s2', 'HIST140'], ['s2', 'BIO130'], ['s3', 'ECON150'], ['s3', 'MATH101H'], ['s3', 'CHEM120'],
     ['s4', 'HIST140'], ['s2', 'PHYS110'], ['s3', 'BIO130']],
    {'MATH101': 3, 'MATH101H': 6, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 5, 'HIST140': 6, 'ECON150': 6}],
   [76, 3, '76/3']),
  ('partial repair guard 3',
   [[['s2', 'PHYS110'], ['s2', 'MATH101H']],
    {'MATH101': 2, 'MATH101H': 4, 'PHYS110': 1, 'CHEM120': 4, 'BIO130': 5, 'HIST140': 3, 'ECON150': 3}],
   [4, 1, '4']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('boundary control 5',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('normal control 6',
   [[['s1', 'CHEM120'], ['s2', 'CHEM120'], ['s2', 'ECON150'], ['s1', 'ECON150'], ['s1', 'MATH101'],
     ['s1', 'CHEM120'], ['s2', 'HIST140'], ['s2', 'BIO130']],
    {'MATH101': 7, 'MATH101H': 4, 'PHYS110': 1, 'CHEM120': 4, 'BIO130': 3, 'HIST140': 5, 'ECON150': 7}],
   [62, 2, '31']),
  ('normal control 7',
   [[['s4', 'CHEM120'], ['s4', 'PHYS110'], ['s5', 'MATH101H'], ['s2', 'CHEM120'], ['s4', 'MATH101'],
     ['s5', 'HIST140'], ['s2', 'ECON150'], ['s2', 'MATH101H'], ['s5', 'CHEM120']],
    {'MATH101': 3, 'MATH101H': 1, 'PHYS110': 1, 'CHEM120': 6, 'BIO130': 7, 'HIST140': 6, 'ECON150': 6}],
   [17, 3, '17/3']),
  ('normal control 8',
   [[['s2', 'PHYS110'], ['s2', 'ECON150']],
    {'MATH101': 6, 'MATH101H': 1, 'PHYS110': 2, 'CHEM120': 2, 'BIO130': 5, 'HIST140': 3, 'ECON150': 1}],
   [16, 1, '16'])],
 [('regression: proximity weight 1',
   [[['s1', 'MATH101'], ['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 2}], [8, 1, '8']),
  ('regression variant: proximity weight 2',
   [[['s5', 'PHYS110'], ['s5', 'BIO130'], ['s4', 'ECON150'], ['s5', 'HIST140'], ['s5', 'PHYS110'],
     ['s5', 'MATH101H'], ['s1', 'CHEM120'], ['s1', 'ECON150'], ['s4', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 4, 'PHYS110': 2, 'CHEM120': 5, 'BIO130': 5, 'HIST140': 3, 'ECON150': 1}],
   [78, 3, '26']),
  ('partial repair guard 3',
   [[['s4', 'ECON150'], ['s4', 'MATH101H'], ['s3', 'MATH101H'], ['s4', 'HIST140'], ['s1', 'PHYS110'],
     ['s4', 'PHYS110'], ['s1', 'BIO130'], ['s1', 'MATH101'], ['s1', 'CHEM120']],
    {'MATH101': 3, 'MATH101H': 7, 'PHYS110': 7, 'CHEM120': 4, 'BIO130': 0, 'HIST140': 7, 'ECON150': 1}],
   [28, 3, '28/3']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s3', 'CHEM120'], ['s4', 'BIO130'], ['s4', 'PHYS110'], ['s3', 'ECON150'], ['s2', 'MATH101'],
     ['s4', 'MATH101H'], ['s3', 'PHYS110']],
    {'MATH101': 3, 'MATH101H': 6, 'PHYS110': 5, 'CHEM120': 3, 'BIO130': 4, 'HIST140': 5, 'ECON150': 7}],
   [58, 3, '58/3']),
  ('normal control 7',
   [[['s3', 'BIO130'], ['s2', 'ECON150'], ['s1', 'ECON150'], ['s3', 'MATH101H'], ['s3', 'PHYS110'],
     ['s2', 'MATH101H'], ['s1', 'CHEM120'], ['s5', 'HIST140']],
    {'MATH101': 2, 'MATH101H': 1, 'PHYS110': 7, 'CHEM120': 0, 'BIO130': 1, 'HIST140': 5, 'ECON150': 1}],
   [16, 4, '4']),
  ('normal control 8',
   [[['s2', 'BIO130'], ['s2', 'HIST140'], ['s2', 'MATH101'], ['s2', 'PHYS110'], ['s5', 'HIST140'],
     ['s3', 'CHEM120'], ['s5', 'ECON150'], ['s3', 'MATH101H'], ['s5', 'MATH101'], ['s5', 'MATH101H'],
     ['s2', 'HIST140']],
    {'MATH101': 1, 'MATH101H': 4, 'PHYS110': 7, 'CHEM120': 2, 'BIO130': 4, 'HIST140': 1, 'ECON150': 6}],
   [38, 3, '38/3'])],
 [('regression: proximity weight 1',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('regression variant: proximity weight 2',
   [[['s4', 'MATH101H'], ['s5', 'MATH101'], ['s5', 'HIST140'], ['s1', 'MATH101H'], ['s1', 'ECON150'],
     ['s1', 'PHYS110'], ['s5', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'PHYS110'], ['s1', 'HIST140'],
     ['s3', 'PHYS110'], ['s5', 'MATH101'], ['s2', 'HIST140'], ['s2', 'BIO130'], ['s4', 'MATH101']],
    {'MATH101': 0, 'MATH101H': 0, 'PHYS110': 5, 'CHEM120': 2, 'BIO130': 3, 'HIST140': 6, 'ECON150': 7}],
   [94, 5, '94/5']),
  ('partial repair guard 3',
   [[['s5', 'CHEM120'], ['s3', 'MATH101H'], ['s2', 'ECON150'], ['s5', 'MATH101H'], ['s1', 'ECON150'],
     ['s4', 'CHEM120'], ['s2', 'CHEM120'], ['s3', 'BIO130'], ['s4', 'PHYS110'], ['s5', 'ECON150'],
     ['s3', 'ECON150'], ['s2', 'PHYS110'], ['s5', 'HIST140'], ['s4', 'MATH101H'], ['s4', 'BIO130'],
     ['s4', 'BIO130'], ['s3', 'HIST140'], ['s2', 'MATH101H']],
    {'MATH101': 3, 'MATH101H': 6, 'PHYS110': 1, 'CHEM120': 1, 'BIO130': 6, 'HIST140': 6, 'ECON150': 5}],
   [110, 5, '22']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('normal control 5',
   [[['s5', 'MATH101'], ['s3', 'BIO130'], ['s5', 'CHEM120'], ['s2', 'ECON150'], ['s2', 'PHYS110'],
     ['s2', 'PHYS110'], ['s2', 'MATH101H']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 6, 'HIST140': 7, 'ECON150': 6}],
   [11, 3, '11/3']),
  ('normal control 6',
   [[['s2', 'HIST140'], ['s2', 'BIO130'], ['s3', 'ECON150'], ['s3', 'MATH101H'], ['s3', 'CHEM120'],
     ['s4', 'HIST140'], ['s2', 'PHYS110'], ['s3', 'BIO130']],
    {'MATH101': 3, 'MATH101H': 6, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 5, 'HIST140': 6, 'ECON150': 6}],
   [76, 3, '76/3']),
  ('normal control 7',
   [[['s5', 'MATH101'], ['s5', 'HIST140'], ['s1', 'HIST140'], ['s1', 'BIO130'], ['s5', 'BIO130'],
     ['s1', 'PHYS110'], ['s2', 'HIST140']],
    {'MATH101': 4, 'MATH101H': 7, 'PHYS110': 7, 'CHEM120': 6, 'BIO130': 3, 'HIST140': 2, 'ECON150': 4}],
   [59, 3, '59/3']),
  ('normal control 8',
   [[['s1', 'MATH101H'], ['s1', 'CHEM120'], ['s3', 'HIST140'], ['s3', 'PHYS110'], ['s3', 'MATH101'],
     ['s3', 'ECON150'], ['s4', 'PHYS110'], ['s3', 'HIST140']],
    {'MATH101': 4, 'MATH101H': 4, 'PHYS110': 6, 'CHEM120': 7, 'BIO130': 0, 'HIST140': 0, 'ECON150': 5}],
   [47, 3, '47/3'])],
 [('regression: proximity weight 1',
   [[['s3', 'CHEM120'], ['s1', 'MATH101'], ['s2', 'CHEM120'], ['s5', 'HIST140'], ['s5', 'BIO130'],
     ['s1', 'HIST140'], ['s1', 'CHEM120'], ['s1', 'BIO130'], ['s3', 'BIO130'], ['s2', 'MATH101H'],
     ['s2', 'MATH101'], ['s2', 'HIST140']],
    {'MATH101': 2, 'MATH101H': 0, 'PHYS110': 3, 'CHEM120': 5, 'BIO130': 4, 'HIST140': 0, 'ECON150': 0}],
   [79, 4, '79/4']),
  ('regression variant: proximity weight 2',
   [[['s5', 'MATH101H'], ['s3', 'HIST140'], ['s4', 'ECON150'], ['s5', 'CHEM120'], ['s4', 'HIST140'],
     ['s5', 'HIST140'], ['s3', 'ECON150'], ['s4', 'ECON150'], ['s3', 'MATH101']],
    {'MATH101': 2, 'MATH101H': 4, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 1, 'HIST140': 1, 'ECON150': 3}],
   [76, 3, '76/3']),
  ('partial repair guard 3',
   [[['s5', 'PHYS110'], ['s5', 'BIO130'], ['s4', 'ECON150'], ['s5', 'HIST140'], ['s5', 'PHYS110'],
     ['s5', 'MATH101H'], ['s1', 'CHEM120'], ['s1', 'ECON150'], ['s4', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 4, 'PHYS110': 2, 'CHEM120': 5, 'BIO130': 5, 'HIST140': 3, 'ECON150': 1}],
   [78, 3, '26']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s2', 'ECON150'], ['s2', 'ECON150'], ['s4', 'MATH101H'], ['s4', 'HIST140'], ['s3', 'HIST140'],
     ['s3', 'PHYS110'], ['s3', 'CHEM120'], ['s3', 'MATH101'], ['s2', 'PHYS110'], ['s4', 'CHEM120'],
     ['s4', 'BIO130'], ['s2', 'CHEM120'], ['s1', 'MATH101']],
    {'MATH101': 7, 'MATH101H': 5, 'PHYS110': 3, 'CHEM120': 2, 'BIO130': 7, 'HIST140': 4, 'ECON150': 5}],
   [116, 4, '29']),
  ('normal control 7',
   [[['s2', 'BIO130'], ['s3', 'ECON150'], ['s4', 'BIO130'], ['s2', 'MATH101H'], ['s1', 'BIO130'],
     ['s1', 'MATH101'], ['s5', 'HIST140'], ['s2', 'MATH101H'], ['s2', 'MATH101'], ['s1', 'PHYS110'],
     ['s4', 'CHEM120'], ['s2', 'ECON150'], ['s1', 'MATH101H']],
    {'MATH101': 6, 'MATH101H': 2, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 4, 'HIST140': 4, 'ECON150': 4}],
   [77, 5, '77/5']),
  ('normal control 8',
   [[['s2', 'PHYS110'], ['s1', 'PHYS110'], ['s2', 'CHEM120'], ['s2', 'ECON150'], ['s1', 'CHEM120'],
     ['s5', 'BIO130'], ['s5', 'ECON150'], ['s1', 'ECON150'], ['s1', 'HIST140'], ['s2', 'BIO130']],
    {'MATH101': 3, 'MATH101H': 5, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 2, 'HIST140': 6, 'ECON150': 1}],
   [67, 3, '67/3'])]]
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 fixture	Actual	Expected	Outcome
regression: proximity weight 1	`[32, 1, '32']`	`[16, 1, '16']`	Failed
regression variant: proximity weight 2	`[106, 4, '53/2']`	`[52, 4, '13']`	Failed
partial repair guard 3	`[238, 4, '119/2']`	`[105, 4, '105/4']`	Failed
boundary control 4	`[0, 1, '0']`	`[0, 1, '0']`	Passed
boundary control 5	`[0, 1, '0']`	`[0, 1, '0']`	Passed
normal control 6	`[172, 3, '172/3']`	`[75, 3, '25']`	Failed
normal control 7	`[164, 4, '41']`	`[80, 4, '20']`	Failed
normal control 8	`[38, 5, '38/5']`	`[14, 5, '14/5']`	Failed

SHA-256 / 7276e02e141612257b6d96759fc196fb5a01bbfa3cf1e267b585614bf868fe79

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:52:04.121717+00:00.

Case digest / a61f6c3d713b44683a44f484c6b0a2a3803a3d0d2acf64e050aafe2a8e94dbaf