FAILURE MAP
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FA-97601 / Knitting and sewing pattern grading / Open access

Quilt binding strip planner: diagonal join loss · case 01

The planner cuts an extra strip because it counts a join on the last strip.

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

ROOT CAUSE

n strips are charged n joins instead of n-1.

THE FAILURE

n strips are charged n joins instead of n-1.

Unsuccessful approach: Doubling the loss per join over-buys.

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 * 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: diagonal join loss', [600, 5, 140, 1, 30], [5, 25, 40]],
  ['repair check: diagonal join loss', [600, 6.5, 140, 1, 25], [5, 32.5, 39.0]],
  ['generated control 1', [200, 6, 140, 0, 25], [2, 12, 49]],
  ['generated control 2', [350, 5, 150, 0, 25], [3, 15, 65]],
  ['generated control 3', [200, 4, 107, 0, 25], [3, 12, 88]]],
 [['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: diagonal join loss', [420, 6, 150, 0, 30], [4, 24, 132]],
  ['repair check: diagonal join loss', [350, 6, 150, 0, 25], [3, 18, 63]],
  ['generated control 1', [420, 4, 140, 0, 30], [4, 16, 98]],
  ['generated control 2', [350, 5, 110, 0, 30], [4, 20, 45]],
  ['generated control 3', [150, 6, 150, 2, 30], [2, 12, 106]]],
 [['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: diagonal join loss', [600, 6, 150, 0, 20], [5, 30, 106]],
  ['repair check: diagonal join loss', [420, 6.5, 150, 0, 30], [4, 26.0, 130.5]],
  ['generated control 1', [150, 6, 150, 0, 25], [2, 12, 119]],
  ['generated control 2', [280, 5, 140, 2, 30], [3, 15, 88]],
  ['generated control 3', [150, 5, 107, 0, 0], [2, 10, 59]]],
 [['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: diagonal join loss', [600, 5, 150, 0, 0], [5, 25, 130]],
  ['repair check: diagonal join loss', [280, 6.5, 107, 0, 30], [4, 26.0, 98.5]],
  ['generated control 1', [420, 4, 110, 1, 0], [4, 16, 0]],
  ['generated control 2', [200, 6.5, 150, 0, 25], [2, 13.0, 68.5]],
  ['generated control 3', [350, 5, 110, 2, 0], [4, 20, 59]]],
 [['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: diagonal join loss', [150, 4, 140, 2, 0], [2, 8, 118]],
  ['repair check: diagonal join loss', [600, 4, 140, 1, 25], [5, 20, 49]],
  ['generated control 1', [280, 6, 107, 1, 30], [4, 24, 92]],
  ['generated control 2', [600, 4, 140, 0, 0], [5, 20, 84]],
  ['generated control 3', [200, 5, 107, 2, 30], [3, 15, 69]]]]
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 fixtureActualExpectedOutcome
baby quilt[3, 18, 1][3, 18, 7]Failed
two strips[2, 12, 4][2, 12, 10]Failed
narrow fabricerror: fabric too narrowerror: fabric too narrowPassed
regression: diagonal join loss[5, 25, 35][5, 25, 40]Failed
repair check: diagonal join loss[5, 32.5, 32.5][5, 32.5, 39.0]Failed
generated control 1[2, 12, 43][2, 12, 49]Failed
generated control 2[3, 15, 60][3, 15, 65]Failed
generated control 3[3, 12, 84][3, 12, 88]Failed

SHA-256 / d4b19e5378a71d51452aa3f3c1902c21e5b9eea213786b2990a798d4b25611d0

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) * 2 * 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: diagonal join loss', [600, 5, 140, 1, 30], [5, 25, 40]],
  ['repair check: diagonal join loss', [600, 6.5, 140, 1, 25], [5, 32.5, 39.0]],
  ['generated control 1', [200, 6, 140, 0, 25], [2, 12, 49]],
  ['generated control 2', [350, 5, 150, 0, 25], [3, 15, 65]],
  ['generated control 3', [200, 4, 107, 0, 25], [3, 12, 88]]],
 [['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: diagonal join loss', [420, 6, 150, 0, 30], [4, 24, 132]],
  ['repair check: diagonal join loss', [350, 6, 150, 0, 25], [3, 18, 63]],
  ['generated control 1', [420, 4, 140, 0, 30], [4, 16, 98]],
  ['generated control 2', [350, 5, 110, 0, 30], [4, 20, 45]],
  ['generated control 3', [150, 6, 150, 2, 30], [2, 12, 106]]],
 [['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: diagonal join loss', [600, 6, 150, 0, 20], [5, 30, 106]],
  ['repair check: diagonal join loss', [420, 6.5, 150, 0, 30], [4, 26.0, 130.5]],
  ['generated control 1', [150, 6, 150, 0, 25], [2, 12, 119]],
  ['generated control 2', [280, 5, 140, 2, 30], [3, 15, 88]],
  ['generated control 3', [150, 5, 107, 0, 0], [2, 10, 59]]],
 [['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: diagonal join loss', [600, 5, 150, 0, 0], [5, 25, 130]],
  ['repair check: diagonal join loss', [280, 6.5, 107, 0, 30], [4, 26.0, 98.5]],
  ['generated control 1', [420, 4, 110, 1, 0], [4, 16, 0]],
  ['generated control 2', [200, 6.5, 150, 0, 25], [2, 13.0, 68.5]],
  ['generated control 3', [350, 5, 110, 2, 0], [4, 20, 59]]],
 [['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: diagonal join loss', [150, 4, 140, 2, 0], [2, 8, 118]],
  ['repair check: diagonal join loss', [600, 4, 140, 1, 25], [5, 20, 49]],
  ['generated control 1', [280, 6, 107, 1, 30], [4, 24, 92]],
  ['generated control 2', [600, 4, 140, 0, 0], [5, 20, 84]],
  ['generated control 3', [200, 5, 107, 2, 30], [3, 15, 69]]]]
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 fixtureActualExpectedOutcome
baby quilt[4, 24, 91][3, 18, 7]Failed
two strips[2, 12, 4][2, 12, 10]Failed
narrow fabricerror: fabric too narrowerror: fabric too narrowPassed
regression: diagonal join loss[5, 25, 20][5, 25, 40]Failed
repair check: diagonal join loss[5, 32.5, 13.0][5, 32.5, 39.0]Failed
generated control 1[2, 12, 43][2, 12, 49]Failed
generated control 2[3, 15, 55][3, 15, 65]Failed
generated control 3[3, 12, 80][3, 12, 88]Failed

SHA-256 / c88526c02349d0fefaa4a07e4f91b683b035359f10b3b073f673abf985731d46

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.

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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 2026-09-29T14:52:33.778154+00:00.

Case digest / 65564fa4f9f9d2d88bed30d1a0b2a01c081ed008f08fb5611cde10be2d9b9065