FA-5726 / Combinatorics / Open access
Nonadjacent subset count fixed size · case 01
Selections containing adjacent positions are not excluded.
ROOT CAUSE
Selections containing adjacent positions are not excluded.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return math.comb(n-k+1,k) if n-k+1>=k else 0
Unsuccessful approach: The gap compression consumes one unnecessary trailing gap.
Case contract
Nonnegative integer counts. Permutation and combination counts are zero when a requested selection exceeds the available objects. Shape sizes satisfy the preconditions stated below. Choose k positions among n linearly ordered positions with no adjacent selected pair. Exact operational definition: math.comb(n-k+1,k) if n-k+1>=k else 0
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Combinatorics results depend on the stated convention.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(n, k):
return math.comb(n,k)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (5, 2)', solve(*(5, 2)), 6)
check('fixture 2: (3, 2)', solve(*(3, 2)), 1)
check('fixture 3: (4, 3)', solve(*(4, 3)), 0)
check('fixture 4: (6, 0)', solve(*(6, 0)), 1)
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 |
|---|---|---|---|
| fixture 1: (5, 2) | 10 | 6 | Failed |
| fixture 2: (3, 2) | 3 | 1 | Failed |
| fixture 3: (4, 3) | 4 | 0 | Failed |
| fixture 4: (6, 0) | 1 | 1 | Passed |
SHA-256 / 3d858e3db838da710c277c8477f9d66628af652b65523c3ab410a0c3ed3fd72b
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(n, k):
return math.comb(n-k,k) if n-k>=k else 0
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (5, 2)', solve(*(5, 2)), 6)
check('fixture 2: (3, 2)', solve(*(3, 2)), 1)
check('fixture 3: (4, 3)', solve(*(4, 3)), 0)
check('fixture 4: (6, 0)', solve(*(6, 0)), 1)
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 |
|---|---|---|---|
| fixture 1: (5, 2) | 3 | 6 | Failed |
| fixture 2: (3, 2) | 0 | 1 | Failed |
| fixture 3: (4, 3) | 0 | 0 | Passed |
| fixture 4: (6, 0) | 1 | 1 | Passed |
SHA-256 / 108d7004462be1e78688ad82907e519b7363c18949053096a4b537abb3e9d2ef
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(n, k):
return math.comb(n-k+1,k) if n-k+1>=k else 0
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (5, 2)', solve(*(5, 2)), 6)
check('fixture 2: (3, 2)', solve(*(3, 2)), 1)
check('fixture 3: (4, 3)', solve(*(4, 3)), 0)
check('fixture 4: (6, 0)', solve(*(6, 0)), 1)
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 |
|---|---|---|---|
| fixture 1: (5, 2) | 6 | 6 | Passed |
| fixture 2: (3, 2) | 1 | 1 | Passed |
| fixture 3: (4, 3) | 0 | 0 | Passed |
| fixture 4: (6, 0) | 1 | 1 | Passed |
SHA-256 / e70cd8e272d539013a0409067d2721e5fb3c419a93336a65cdaeb83b6a78a7df
Verification & scope
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 2026-09-29T14:37:52.826696+00:00.
Case digest / 99b4ad6c94e2aea534f3fe5c060720471b81303d4f722dda165a3515a75f59ed