FA-97596 / Knitting and sewing pattern grading / Open access

Quilt binding strip planner: selvage trim both edges · case 01

Binding comes up short because only one selvage was trimmed in the plan.

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

ROOT CAUSE

Only one selvage is removed from the strip length.

VERIFIED REPAIR

Trim a selvage from each end.

Unsuccessful approach: An extra centimetre of trim is not in the contract and over-cuts.

Case contract

Usable strip length = fabric_width - 2*selvage. Joining n strips with diagonal seams loses strip_width per join (n-1 joins). Need perimeter + tail. n is the smallest count with n*usable - (n-1)*strip_width >= need. Return [n, fabric cut length n*strip_width, surplus]; usable <= strip_width -> "error: fabric too narrow".

Why this case matters

Quilters cut width-of-fabric strips and join them diagonally to bind the quilt edge.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(perimeter, strip_width, fabric_width, selvage, tail):
    usable = fabric_width - selvage
    if usable <= strip_width:
        return 'error: fabric too narrow'
    need = perimeter + tail
    def length(n):
        return n * usable - (n - 1) * strip_width
    n = 1
    while length(n) < need:
        n += 1
    return [n, n * strip_width, length(n) - need]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]], ['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['regression: selvage trim both edges', [420, 5, 107, 1, 0], [5, 25, 85]],
  ['repair check: selvage trim both edges', [420, 6, 150, 2, 30], [4, 24, 116]],
  ['generated control 1', [600, 5, 140, 2, 0], [5, 25, 60]],
  ['generated control 2', [200, 6.5, 110, 0, 20], [3, 19.5, 97.0]],
  ['generated control 3', [420, 6, 150, 1, 30], [4, 24, 124]]],
 [['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]],
  ['regression: selvage trim both edges', [420, 5, 107, 2, 20], [5, 25, 55]],
  ['repair check: selvage trim both edges', [200, 5, 107, 0, 0], [2, 10, 9]],
  ['generated control 1', [600, 6, 110, 1, 25], [7, 42, 95]],
  ['generated control 2', [420, 6, 110, 1, 30], [5, 30, 66]],
  ['generated control 3', [350, 6.5, 150, 2, 20], [3, 19.5, 55.0]]],
 [['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]], ['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['regression: selvage trim both edges', [150, 4, 110, 1, 20], [2, 8, 42]],
  ['repair check: selvage trim both edges', [200, 4, 150, 1, 25], [2, 8, 67]],
  ['generated control 1', [150, 6, 110, 1, 25], [2, 12, 35]],
  ['generated control 2', [600, 5, 107, 0, 25], [7, 35, 94]],
  ['generated control 3', [150, 6.5, 107, 2, 0], [2, 13.0, 49.5]]],
 [['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]], ['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['regression: selvage trim both edges', [150, 6, 107, 2, 25], [2, 12, 25]],
  ['repair check: selvage trim both edges', [420, 5, 110, 1, 25], [5, 25, 75]],
  ['generated control 1', [420, 6.5, 110, 2, 25], [5, 32.5, 59.0]],
  ['generated control 2', [200, 5, 140, 1, 30], [2, 10, 41]],
  ['generated control 3', [600, 6.5, 140, 1, 20], [5, 32.5, 44.0]]],
 [['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]],
  ['regression: selvage trim both edges', [150, 6, 150, 1, 25], [2, 12, 115]],
  ['repair check: selvage trim both edges', [420, 4, 107, 1, 0], [5, 20, 89]],
  ['generated control 1', [280, 6.5, 150, 0, 30], [3, 19.5, 127.0]],
  ['generated control 2', [600, 4, 107, 2, 25], [7, 28, 72]],
  ['generated control 3', [350, 5, 107, 0, 30], [4, 20, 33]]]]
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
baby quilt	`[3, 18, 10]`	`[3, 18, 7]`	Failed
two strips	`[2, 12, 14]`	`[2, 12, 10]`	Failed
narrow fabric	`error: fabric too narrow`	`error: fabric too narrow`	Passed
regression: selvage trim both edges	`[5, 25, 90]`	`[5, 25, 85]`	Failed
repair check: selvage trim both edges	`[4, 24, 124]`	`[4, 24, 116]`	Failed
generated control 1	`[5, 25, 70]`	`[5, 25, 60]`	Failed
generated control 2	`[3, 19.5, 97.0]`	`[3, 19.5, 97.0]`	Passed
generated control 3	`[4, 24, 128]`	`[4, 24, 124]`	Failed

SHA-256 / 81ecb06c22b095ac38e322a471fa36bc170257d45a41f69d6aef0c44564a0887

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(perimeter, strip_width, fabric_width, selvage, tail):
    usable = fabric_width - 2 * selvage - 1
    if usable <= strip_width:
        return 'error: fabric too narrow'
    need = perimeter + tail
    def length(n):
        return n * usable - (n - 1) * strip_width
    n = 1
    while length(n) < need:
        n += 1
    return [n, n * strip_width, length(n) - need]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]], ['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['regression: selvage trim both edges', [420, 5, 107, 1, 0], [5, 25, 85]],
  ['repair check: selvage trim both edges', [420, 6, 150, 2, 30], [4, 24, 116]],
  ['generated control 1', [600, 5, 140, 2, 0], [5, 25, 60]],
  ['generated control 2', [200, 6.5, 110, 0, 20], [3, 19.5, 97.0]],
  ['generated control 3', [420, 6, 150, 1, 30], [4, 24, 124]]],
 [['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]],
  ['regression: selvage trim both edges', [420, 5, 107, 2, 20], [5, 25, 55]],
  ['repair check: selvage trim both edges', [200, 5, 107, 0, 0], [2, 10, 9]],
  ['generated control 1', [600, 6, 110, 1, 25], [7, 42, 95]],
  ['generated control 2', [420, 6, 110, 1, 30], [5, 30, 66]],
  ['generated control 3', [350, 6.5, 150, 2, 20], [3, 19.5, 55.0]]],
 [['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]], ['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['regression: selvage trim both edges', [150, 4, 110, 1, 20], [2, 8, 42]],
  ['repair check: selvage trim both edges', [200, 4, 150, 1, 25], [2, 8, 67]],
  ['generated control 1', [150, 6, 110, 1, 25], [2, 12, 35]],
  ['generated control 2', [600, 5, 107, 0, 25], [7, 35, 94]],
  ['generated control 3', [150, 6.5, 107, 2, 0], [2, 13.0, 49.5]]],
 [['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]], ['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['regression: selvage trim both edges', [150, 6, 107, 2, 25], [2, 12, 25]],
  ['repair check: selvage trim both edges', [420, 5, 110, 1, 25], [5, 25, 75]],
  ['generated control 1', [420, 6.5, 110, 2, 25], [5, 32.5, 59.0]],
  ['generated control 2', [200, 5, 140, 1, 30], [2, 10, 41]],
  ['generated control 3', [600, 6.5, 140, 1, 20], [5, 32.5, 44.0]]],
 [['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]],
  ['regression: selvage trim both edges', [150, 6, 150, 1, 25], [2, 12, 115]],
  ['repair check: selvage trim both edges', [420, 4, 107, 1, 0], [5, 20, 89]],
  ['generated control 1', [280, 6.5, 150, 0, 30], [3, 19.5, 127.0]],
  ['generated control 2', [600, 4, 107, 2, 25], [7, 28, 72]],
  ['generated control 3', [350, 5, 107, 0, 30], [4, 20, 33]]]]
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
baby quilt	`[3, 18, 4]`	`[3, 18, 7]`	Failed
two strips	`[2, 12, 8]`	`[2, 12, 10]`	Failed
narrow fabric	`error: fabric too narrow`	`error: fabric too narrow`	Passed
regression: selvage trim both edges	`[5, 25, 80]`	`[5, 25, 85]`	Failed
repair check: selvage trim both edges	`[4, 24, 112]`	`[4, 24, 116]`	Failed
generated control 1	`[5, 25, 55]`	`[5, 25, 60]`	Failed
generated control 2	`[3, 19.5, 94.0]`	`[3, 19.5, 97.0]`	Failed
generated control 3	`[4, 24, 120]`	`[4, 24, 124]`	Failed

SHA-256 / 392ecac85b7f339e93457f06f6f0c19f805da8a2698289da89a23391fb91301d

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(perimeter, strip_width, fabric_width, selvage, tail):
    usable = fabric_width - 2 * selvage
    if usable <= strip_width:
        return 'error: fabric too narrow'
    need = perimeter + tail
    def length(n):
        return n * usable - (n - 1) * strip_width
    n = 1
    while length(n) < need:
        n += 1
    return [n, n * strip_width, length(n) - need]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]], ['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['regression: selvage trim both edges', [420, 5, 107, 1, 0], [5, 25, 85]],
  ['repair check: selvage trim both edges', [420, 6, 150, 2, 30], [4, 24, 116]],
  ['generated control 1', [600, 5, 140, 2, 0], [5, 25, 60]],
  ['generated control 2', [200, 6.5, 110, 0, 20], [3, 19.5, 97.0]],
  ['generated control 3', [420, 6, 150, 1, 30], [4, 24, 124]]],
 [['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]],
  ['regression: selvage trim both edges', [420, 5, 107, 2, 20], [5, 25, 55]],
  ['repair check: selvage trim both edges', [200, 5, 107, 0, 0], [2, 10, 9]],
  ['generated control 1', [600, 6, 110, 1, 25], [7, 42, 95]],
  ['generated control 2', [420, 6, 110, 1, 30], [5, 30, 66]],
  ['generated control 3', [350, 6.5, 150, 2, 20], [3, 19.5, 55.0]]],
 [['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]], ['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['regression: selvage trim both edges', [150, 4, 110, 1, 20], [2, 8, 42]],
  ['repair check: selvage trim both edges', [200, 4, 150, 1, 25], [2, 8, 67]],
  ['generated control 1', [150, 6, 110, 1, 25], [2, 12, 35]],
  ['generated control 2', [600, 5, 107, 0, 25], [7, 35, 94]],
  ['generated control 3', [150, 6.5, 107, 2, 0], [2, 13.0, 49.5]]],
 [['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]], ['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['regression: selvage trim both edges', [150, 6, 107, 2, 25], [2, 12, 25]],
  ['repair check: selvage trim both edges', [420, 5, 110, 1, 25], [5, 25, 75]],
  ['generated control 1', [420, 6.5, 110, 2, 25], [5, 32.5, 59.0]],
  ['generated control 2', [200, 5, 140, 1, 30], [2, 10, 41]],
  ['generated control 3', [600, 6.5, 140, 1, 20], [5, 32.5, 44.0]]],
 [['two strips', [196, 6, 110, 2, 0], [2, 12, 10]],
  ['narrow fabric', [100, 6, 6, 0, 0], 'error: fabric too narrow'],
  ['baby quilt', [280, 6, 110, 1, 25], [3, 18, 7]],
  ['regression: selvage trim both edges', [150, 6, 150, 1, 25], [2, 12, 115]],
  ['repair check: selvage trim both edges', [420, 4, 107, 1, 0], [5, 20, 89]],
  ['generated control 1', [280, 6.5, 150, 0, 30], [3, 19.5, 127.0]],
  ['generated control 2', [600, 4, 107, 2, 25], [7, 28, 72]],
  ['generated control 3', [350, 5, 107, 0, 30], [4, 20, 33]]]]
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
baby quilt	`[3, 18, 7]`	`[3, 18, 7]`	Passed
two strips	`[2, 12, 10]`	`[2, 12, 10]`	Passed
narrow fabric	`error: fabric too narrow`	`error: fabric too narrow`	Passed
regression: selvage trim both edges	`[5, 25, 85]`	`[5, 25, 85]`	Passed
repair check: selvage trim both edges	`[4, 24, 116]`	`[4, 24, 116]`	Passed
generated control 1	`[5, 25, 60]`	`[5, 25, 60]`	Passed
generated control 2	`[3, 19.5, 97.0]`	`[3, 19.5, 97.0]`	Passed
generated control 3	`[4, 24, 124]`	`[4, 24, 124]`	Passed

SHA-256 / f3276aea5fb34168a7eba894c0c85724c04babc5d37fc776ee42f854ec34e6bb

Verification & scope

A deterministic toy contract stated in full here; it is a bounded teaching model, not an authoritative reference or standards implementation. 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 2026-09-29T14:52:33.709188+00:00.

Case digest / 819618a09cc9838e2d5b012372a7fac9e14f6d74cf5d45501c7cd32a542d71b0