FA-97606 / Knitting and sewing pattern grading / Open access

Quilt binding strip planner: finishing tail · case 01

The binding exactly matches the perimeter, leaving nothing to join the ends.

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

ROOT CAUSE

The tail allowance for joining the ends is not added.

VERIFIED REPAIR

Need perimeter plus tail.

Unsuccessful approach: Half the tail is not enough to join the ends.

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
    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: finishing tail', [150, 5, 107, 2, 20], [2, 10, 31]],
  ['repair check: finishing tail', [420, 4, 110, 2, 20], [5, 20, 74]],
  ['generated control 1', [150, 6, 150, 1, 30], [2, 12, 110]],
  ['generated control 2', [150, 6.5, 150, 0, 0], [1, 6.5, 0.0]],
  ['generated control 3', [150, 4, 107, 2, 0], [2, 8, 52]]],
 [['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: finishing tail', [420, 4, 150, 1, 30], [4, 16, 130]],
  ['repair check: finishing tail', [420, 5, 140, 2, 30], [4, 20, 79]],
  ['generated control 1', [350, 4, 110, 1, 20], [4, 16, 50]],
  ['generated control 2', [350, 5, 107, 1, 25], [4, 20, 30]],
  ['generated control 3', [280, 6, 110, 1, 20], [3, 18, 12]]],
 [['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: finishing tail', [150, 6, 107, 0, 20], [2, 12, 38]],
  ['repair check: finishing tail', [350, 6.5, 140, 1, 20], [3, 19.5, 31.0]],
  ['generated control 1', [600, 6, 110, 1, 25], [7, 42, 95]],
  ['generated control 2', [150, 6.5, 110, 2, 0], [2, 13.0, 55.5]],
  ['generated control 3', [600, 4, 150, 0, 30], [5, 20, 104]]],
 [['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: finishing tail', [280, 4, 150, 2, 20], [3, 12, 130]],
  ['repair check: finishing tail', [420, 6.5, 107, 2, 25], [5, 32.5, 44.0]],
  ['generated control 1', [200, 6.5, 150, 2, 0], [2, 13.0, 85.5]],
  ['generated control 2', [420, 5, 150, 1, 0], [3, 15, 14]],
  ['generated control 3', [200, 6.5, 107, 2, 30], [3, 19.5, 66.0]]],
 [['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: finishing tail', [350, 4, 107, 2, 20], [4, 16, 30]],
  ['repair check: finishing tail', [420, 6.5, 140, 0, 25], [4, 26.0, 95.5]],
  ['generated control 1', [350, 5, 140, 1, 0], [3, 15, 54]],
  ['generated control 2', [600, 6.5, 110, 2, 20], [7, 45.5, 83.0]],
  ['generated control 3', [150, 5, 140, 1, 20], [2, 10, 101]]]]
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, 32]`	`[3, 18, 7]`	Failed
two strips	`[2, 12, 10]`	`[2, 12, 10]`	Passed
narrow fabric	`error: fabric too narrow`	`error: fabric too narrow`	Passed
regression: finishing tail	`[2, 10, 51]`	`[2, 10, 31]`	Failed
repair check: finishing tail	`[5, 20, 94]`	`[5, 20, 74]`	Failed
generated control 1	`[2, 12, 140]`	`[2, 12, 110]`	Failed
generated control 2	`[1, 6.5, 0.0]`	`[1, 6.5, 0.0]`	Passed
generated control 3	`[2, 8, 52]`	`[2, 8, 52]`	Passed

SHA-256 / 92f665cb6d7bcbf574d7918e0a6a7b309d384b35eb821d3add709c73aea8ba53

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 // 2
    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: finishing tail', [150, 5, 107, 2, 20], [2, 10, 31]],
  ['repair check: finishing tail', [420, 4, 110, 2, 20], [5, 20, 74]],
  ['generated control 1', [150, 6, 150, 1, 30], [2, 12, 110]],
  ['generated control 2', [150, 6.5, 150, 0, 0], [1, 6.5, 0.0]],
  ['generated control 3', [150, 4, 107, 2, 0], [2, 8, 52]]],
 [['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: finishing tail', [420, 4, 150, 1, 30], [4, 16, 130]],
  ['repair check: finishing tail', [420, 5, 140, 2, 30], [4, 20, 79]],
  ['generated control 1', [350, 4, 110, 1, 20], [4, 16, 50]],
  ['generated control 2', [350, 5, 107, 1, 25], [4, 20, 30]],
  ['generated control 3', [280, 6, 110, 1, 20], [3, 18, 12]]],
 [['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: finishing tail', [150, 6, 107, 0, 20], [2, 12, 38]],
  ['repair check: finishing tail', [350, 6.5, 140, 1, 20], [3, 19.5, 31.0]],
  ['generated control 1', [600, 6, 110, 1, 25], [7, 42, 95]],
  ['generated control 2', [150, 6.5, 110, 2, 0], [2, 13.0, 55.5]],
  ['generated control 3', [600, 4, 150, 0, 30], [5, 20, 104]]],
 [['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: finishing tail', [280, 4, 150, 2, 20], [3, 12, 130]],
  ['repair check: finishing tail', [420, 6.5, 107, 2, 25], [5, 32.5, 44.0]],
  ['generated control 1', [200, 6.5, 150, 2, 0], [2, 13.0, 85.5]],
  ['generated control 2', [420, 5, 150, 1, 0], [3, 15, 14]],
  ['generated control 3', [200, 6.5, 107, 2, 30], [3, 19.5, 66.0]]],
 [['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: finishing tail', [350, 4, 107, 2, 20], [4, 16, 30]],
  ['repair check: finishing tail', [420, 6.5, 140, 0, 25], [4, 26.0, 95.5]],
  ['generated control 1', [350, 5, 140, 1, 0], [3, 15, 54]],
  ['generated control 2', [600, 6.5, 110, 2, 20], [7, 45.5, 83.0]],
  ['generated control 3', [150, 5, 140, 1, 20], [2, 10, 101]]]]
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, 20]`	`[3, 18, 7]`	Failed
two strips	`[2, 12, 10]`	`[2, 12, 10]`	Passed
narrow fabric	`error: fabric too narrow`	`error: fabric too narrow`	Passed
regression: finishing tail	`[2, 10, 41]`	`[2, 10, 31]`	Failed
repair check: finishing tail	`[5, 20, 84]`	`[5, 20, 74]`	Failed
generated control 1	`[2, 12, 125]`	`[2, 12, 110]`	Failed
generated control 2	`[1, 6.5, 0.0]`	`[1, 6.5, 0.0]`	Passed
generated control 3	`[2, 8, 52]`	`[2, 8, 52]`	Passed

SHA-256 / c05e0b56fa08a90f5b03bb162e3bff875b62e8ed827dff8317033123cb98ca13

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: finishing tail', [150, 5, 107, 2, 20], [2, 10, 31]],
  ['repair check: finishing tail', [420, 4, 110, 2, 20], [5, 20, 74]],
  ['generated control 1', [150, 6, 150, 1, 30], [2, 12, 110]],
  ['generated control 2', [150, 6.5, 150, 0, 0], [1, 6.5, 0.0]],
  ['generated control 3', [150, 4, 107, 2, 0], [2, 8, 52]]],
 [['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: finishing tail', [420, 4, 150, 1, 30], [4, 16, 130]],
  ['repair check: finishing tail', [420, 5, 140, 2, 30], [4, 20, 79]],
  ['generated control 1', [350, 4, 110, 1, 20], [4, 16, 50]],
  ['generated control 2', [350, 5, 107, 1, 25], [4, 20, 30]],
  ['generated control 3', [280, 6, 110, 1, 20], [3, 18, 12]]],
 [['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: finishing tail', [150, 6, 107, 0, 20], [2, 12, 38]],
  ['repair check: finishing tail', [350, 6.5, 140, 1, 20], [3, 19.5, 31.0]],
  ['generated control 1', [600, 6, 110, 1, 25], [7, 42, 95]],
  ['generated control 2', [150, 6.5, 110, 2, 0], [2, 13.0, 55.5]],
  ['generated control 3', [600, 4, 150, 0, 30], [5, 20, 104]]],
 [['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: finishing tail', [280, 4, 150, 2, 20], [3, 12, 130]],
  ['repair check: finishing tail', [420, 6.5, 107, 2, 25], [5, 32.5, 44.0]],
  ['generated control 1', [200, 6.5, 150, 2, 0], [2, 13.0, 85.5]],
  ['generated control 2', [420, 5, 150, 1, 0], [3, 15, 14]],
  ['generated control 3', [200, 6.5, 107, 2, 30], [3, 19.5, 66.0]]],
 [['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: finishing tail', [350, 4, 107, 2, 20], [4, 16, 30]],
  ['repair check: finishing tail', [420, 6.5, 140, 0, 25], [4, 26.0, 95.5]],
  ['generated control 1', [350, 5, 140, 1, 0], [3, 15, 54]],
  ['generated control 2', [600, 6.5, 110, 2, 20], [7, 45.5, 83.0]],
  ['generated control 3', [150, 5, 140, 1, 20], [2, 10, 101]]]]
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: finishing tail	`[2, 10, 31]`	`[2, 10, 31]`	Passed
repair check: finishing tail	`[5, 20, 74]`	`[5, 20, 74]`	Passed
generated control 1	`[2, 12, 110]`	`[2, 12, 110]`	Passed
generated control 2	`[1, 6.5, 0.0]`	`[1, 6.5, 0.0]`	Passed
generated control 3	`[2, 8, 52]`	`[2, 8, 52]`	Passed

SHA-256 / 7a6a91adef7246afb18141e380f277a333f2403e5a2ac3117d01d45922d9460d

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 2026-09-29T14:52:33.777692+00:00.

Case digest / 80f7039b875616cca411b9c34d552459a2bbdab13a9913acca6f2912571936a8