FA-97611 / Knitting and sewing pattern grading / Open access

Quilt binding strip planner: strip count loop · case 01

An exact fit plans one more strip than needed.

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

ROOT CAUSE

The loop continues on equality.

VERIFIED REPAIR

Stop as soon as the length meets the need.

Unsuccessful approach: Looking one strip ahead stops one strip early.

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 - 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: strip count loop', [280, 6.5, 110, 2, 25], [3, 19.5, 0.0]],
  ['repair check: strip count loop', [200, 6.5, 110, 1, 0], [2, 13.0, 9.5]],
  ['generated control 1', [150, 4, 150, 2, 20], [2, 8, 118]],
  ['generated control 2', [200, 6.5, 150, 2, 20], [2, 13.0, 65.5]],
  ['generated control 3', [350, 6.5, 140, 1, 20], [3, 19.5, 31.0]]],
 [['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: strip count loop', [420, 5, 150, 0, 20], [3, 15, 0]],
  ['repair check: strip count loop', [280, 6.5, 110, 1, 20], [3, 19.5, 11.0]],
  ['generated control 1', [280, 5, 110, 2, 25], [3, 15, 3]],
  ['generated control 2', [420, 6.5, 140, 1, 30], [4, 26.0, 82.5]],
  ['generated control 3', [420, 5, 110, 1, 30], [5, 25, 70]]],
 [['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: strip count loop', [420, 5, 150, 0, 20], [3, 15, 0]],
  ['repair check: strip count loop', [350, 5, 110, 2, 20], [4, 20, 39]],
  ['generated control 1', [350, 5, 150, 0, 20], [3, 15, 70]],
  ['generated control 2', [200, 6.5, 107, 2, 0], [3, 19.5, 96.0]],
  ['generated control 3', [420, 6, 150, 0, 20], [4, 24, 142]]],
 [['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: strip count loop', [280, 5, 107, 1, 25], [3, 15, 0]],
  ['repair check: strip count loop', [150, 6, 150, 0, 20], [2, 12, 124]],
  ['generated control 1', [200, 6.5, 110, 0, 20], [3, 19.5, 97.0]],
  ['generated control 2', [150, 4, 107, 2, 25], [2, 8, 27]],
  ['generated control 3', [600, 4, 150, 0, 0], [5, 20, 134]]],
 [['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: strip count loop', [420, 4, 110, 1, 0], [4, 16, 0]],
  ['repair check: strip count loop', [600, 5, 110, 1, 0], [6, 30, 23]],
  ['generated control 1', [200, 6, 140, 1, 25], [2, 12, 45]],
  ['generated control 2', [200, 6, 150, 1, 25], [2, 12, 65]],
  ['generated control 3', [420, 5, 110, 2, 30], [5, 25, 60]]]]
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: strip count loop	`[4, 26.0, 99.5]`	`[3, 19.5, 0.0]`	Failed
repair check: strip count loop	`[2, 13.0, 9.5]`	`[2, 13.0, 9.5]`	Passed
generated control 1	`[2, 8, 118]`	`[2, 8, 118]`	Passed
generated control 2	`[2, 13.0, 65.5]`	`[2, 13.0, 65.5]`	Passed
generated control 3	`[3, 19.5, 31.0]`	`[3, 19.5, 31.0]`	Passed

SHA-256 / cd352e53bde2484f9bd893bfdb43266527a4646319f52639ca6bfb04726c881c

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
    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 + 1) < 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: strip count loop', [280, 6.5, 110, 2, 25], [3, 19.5, 0.0]],
  ['repair check: strip count loop', [200, 6.5, 110, 1, 0], [2, 13.0, 9.5]],
  ['generated control 1', [150, 4, 150, 2, 20], [2, 8, 118]],
  ['generated control 2', [200, 6.5, 150, 2, 20], [2, 13.0, 65.5]],
  ['generated control 3', [350, 6.5, 140, 1, 20], [3, 19.5, 31.0]]],
 [['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: strip count loop', [420, 5, 150, 0, 20], [3, 15, 0]],
  ['repair check: strip count loop', [280, 6.5, 110, 1, 20], [3, 19.5, 11.0]],
  ['generated control 1', [280, 5, 110, 2, 25], [3, 15, 3]],
  ['generated control 2', [420, 6.5, 140, 1, 30], [4, 26.0, 82.5]],
  ['generated control 3', [420, 5, 110, 1, 30], [5, 25, 70]]],
 [['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: strip count loop', [420, 5, 150, 0, 20], [3, 15, 0]],
  ['repair check: strip count loop', [350, 5, 110, 2, 20], [4, 20, 39]],
  ['generated control 1', [350, 5, 150, 0, 20], [3, 15, 70]],
  ['generated control 2', [200, 6.5, 107, 2, 0], [3, 19.5, 96.0]],
  ['generated control 3', [420, 6, 150, 0, 20], [4, 24, 142]]],
 [['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: strip count loop', [280, 5, 107, 1, 25], [3, 15, 0]],
  ['repair check: strip count loop', [150, 6, 150, 0, 20], [2, 12, 124]],
  ['generated control 1', [200, 6.5, 110, 0, 20], [3, 19.5, 97.0]],
  ['generated control 2', [150, 4, 107, 2, 25], [2, 8, 27]],
  ['generated control 3', [600, 4, 150, 0, 0], [5, 20, 134]]],
 [['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: strip count loop', [420, 4, 110, 1, 0], [4, 16, 0]],
  ['repair check: strip count loop', [600, 5, 110, 1, 0], [6, 30, 23]],
  ['generated control 1', [200, 6, 140, 1, 25], [2, 12, 45]],
  ['generated control 2', [200, 6, 150, 1, 25], [2, 12, 65]],
  ['generated control 3', [420, 5, 110, 2, 30], [5, 25, 60]]]]
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	`[2, 12, -95]`	`[3, 18, 7]`	Failed
two strips	`[1, 6, -90]`	`[2, 12, 10]`	Failed
narrow fabric	`error: fabric too narrow`	`error: fabric too narrow`	Passed
regression: strip count loop	`[2, 13.0, -99.5]`	`[3, 19.5, 0.0]`	Failed
repair check: strip count loop	`[1, 6.5, -92.0]`	`[2, 13.0, 9.5]`	Failed
generated control 1	`[1, 4, -24]`	`[2, 8, 118]`	Failed
generated control 2	`[1, 6.5, -74.0]`	`[2, 13.0, 65.5]`	Failed
generated control 3	`[2, 13.0, -100.5]`	`[3, 19.5, 31.0]`	Failed

SHA-256 / ce20016f683336fd795a80209c29bee454eb333ec8674ecac84b1eb6794706c8

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: strip count loop', [280, 6.5, 110, 2, 25], [3, 19.5, 0.0]],
  ['repair check: strip count loop', [200, 6.5, 110, 1, 0], [2, 13.0, 9.5]],
  ['generated control 1', [150, 4, 150, 2, 20], [2, 8, 118]],
  ['generated control 2', [200, 6.5, 150, 2, 20], [2, 13.0, 65.5]],
  ['generated control 3', [350, 6.5, 140, 1, 20], [3, 19.5, 31.0]]],
 [['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: strip count loop', [420, 5, 150, 0, 20], [3, 15, 0]],
  ['repair check: strip count loop', [280, 6.5, 110, 1, 20], [3, 19.5, 11.0]],
  ['generated control 1', [280, 5, 110, 2, 25], [3, 15, 3]],
  ['generated control 2', [420, 6.5, 140, 1, 30], [4, 26.0, 82.5]],
  ['generated control 3', [420, 5, 110, 1, 30], [5, 25, 70]]],
 [['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: strip count loop', [420, 5, 150, 0, 20], [3, 15, 0]],
  ['repair check: strip count loop', [350, 5, 110, 2, 20], [4, 20, 39]],
  ['generated control 1', [350, 5, 150, 0, 20], [3, 15, 70]],
  ['generated control 2', [200, 6.5, 107, 2, 0], [3, 19.5, 96.0]],
  ['generated control 3', [420, 6, 150, 0, 20], [4, 24, 142]]],
 [['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: strip count loop', [280, 5, 107, 1, 25], [3, 15, 0]],
  ['repair check: strip count loop', [150, 6, 150, 0, 20], [2, 12, 124]],
  ['generated control 1', [200, 6.5, 110, 0, 20], [3, 19.5, 97.0]],
  ['generated control 2', [150, 4, 107, 2, 25], [2, 8, 27]],
  ['generated control 3', [600, 4, 150, 0, 0], [5, 20, 134]]],
 [['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: strip count loop', [420, 4, 110, 1, 0], [4, 16, 0]],
  ['repair check: strip count loop', [600, 5, 110, 1, 0], [6, 30, 23]],
  ['generated control 1', [200, 6, 140, 1, 25], [2, 12, 45]],
  ['generated control 2', [200, 6, 150, 1, 25], [2, 12, 65]],
  ['generated control 3', [420, 5, 110, 2, 30], [5, 25, 60]]]]
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: strip count loop	`[3, 19.5, 0.0]`	`[3, 19.5, 0.0]`	Passed
repair check: strip count loop	`[2, 13.0, 9.5]`	`[2, 13.0, 9.5]`	Passed
generated control 1	`[2, 8, 118]`	`[2, 8, 118]`	Passed
generated control 2	`[2, 13.0, 65.5]`	`[2, 13.0, 65.5]`	Passed
generated control 3	`[3, 19.5, 31.0]`	`[3, 19.5, 31.0]`	Passed

SHA-256 / 627e3fb67df22414b8504d6e98d3ce6b81a9b2c797bb0d260b380445f8e55068

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 2026-09-29T14:52:33.867297+00:00.

Case digest / 4e5c902c4ea8870ccf37998cf6f5c7d1841752c0ee5e459e6b36794c626bd618