Cross-Check a Rectangular Jigsaw's Sorted Border Pieces — Free
Before searching the floor for a lost corner, check whether the sorted edge pile matches the actual piece grid. Keep an excess count distinct from a short count, and handle narrow puzzles without double-counting corners.
The proof surface
Board-game timing tools plan an evening. This stub reconciles rectangular jigsaw geometry and an observed sorted pile. It includes one-row and one-column layouts, displays direction, and never treats an advertised box total as proof of the cut pattern.
InputPuzzle code | columns of pieces | rows of pieces | sorted border count; reader-selected border discrepancy review mark (pieces)
Rare deviceBoard-game timing tools plan an evening. This stub reconciles rectangular jigsaw geometry and an observed sorted pile. It includes one-row and one-column layouts, displays direction, and never treats an advertised box total as proof of the cut pattern.
Output artifactSum of absolute border-pile discrepancies with row-by-row context
Cost$0 local calculation · no card, paid key, subscription or signup · proposed filing price is not for sale
Sample, not your facts: Illustrative inputs: Harbor puzzle | 30 | 20 | 92; Orchard puzzle | 12 | 8 | 36. Reader-selected border discrepancy review mark (pieces) = 0. Sum of absolute border-pile discrepancies: 4 pieces absolute discrepancy. All records are invented.
Before using the puzzle-edge stub
Count actual columns and rows from a confirmed layout, not from dividing an approximate box total. The model assumes a complete rectangular grid with one piece at each position and recognizable border pieces. Irregular novelty cuts, shaped puzzles, missing grid positions and pieces that span several nominal positions do not fit it. The observed border count may be mistaken even when total pieces match the box. A positive signed difference means fewer pieces in the border pile than modeled border positions; a negative difference means an excess in that pile. The review mark is a personal sorting threshold. It is not a manufacturer defect criterion, and no family member is blamed by an arithmetic mismatch.
Why the flat version breaks
Counting corners twice
The common perimeter expression requires correcting for four double-counted corners and still fails on one-row layouts. Counting border as total minus interior avoids both errors. The piece pile should include each physical corner exactly once, regardless of how many sides it touches.
Inferring dimensions from an approximate advertised count
A 600-piece label does not identify a unique 30-by-20 grid, and some boxes use approximate totals. The edge expectation depends on dimensions, not merely total count. Confirm the actual pattern before interpreting the signed discrepancy as a sorting problem.
Calling a mismatch proof of missing pieces
An excess often indicates sorting or dimensions, and a shortage can mean edge pieces remain in another pile. The stub cannot inspect the puzzle. Preserve the sign and investigate the model assumptions before making a replacement request or attributing the gap to a lost piece.
How to work the puzzle-edge stub
Confirm the grid, not just the box total
Use a reliable piece layout or a completed reference to identify whole columns and rows. Several rectangular shapes can have the same total piece count but different borders. If dimensions are uncertain, keep the uncertainty visible and try separately labeled scenarios rather than choosing the one that makes the edge pile appear correct.
Count the sorted pile once
Include corners in the observed border count; each corner is one piece, not one piece for each neighboring side. Enter a whole count no greater than the modeled total number of pieces. Keep separate puzzles in separate rows so a surplus from one cannot silently make another puzzle appear complete.
Subtract interior positions from total positions
Total positions are columns times rows. Interior positions are max(columns-2,0) times max(rows-2,0). Their difference is the modeled border. Subtract the observed edge-pile count for a signed discrepancy and use its absolute value for review. The summary adds those absolute values; a surplus and a shortage cannot cancel each other.
Inspect the relevant pile or layout
For a positive gap, look for edge pieces among the unsorted or interior piles before deciding something was lost. For a negative gap, recheck whether a piece was misclassified or the grid was miscounted. If the puzzle cut is irregular, ask the maker for its piece layout; this model is deliberately narrower than a general missing-piece detector.
What the puzzle-edge stub separates
Question
Before
Inspect this instead
Counting corners twice
The common perimeter expression requires correcting for four double-counted corners and still fails on one-row layouts. Counting border as total minus interior avoids both errors. The piece pile should include each physical corner exactly once, regardless of how many sides it touches.
Count the sorted pile once
Inferring dimensions from an approximate advertised count
A 600-piece label does not identify a unique 30-by-20 grid, and some boxes use approximate totals. The edge expectation depends on dimensions, not merely total count. Confirm the actual pattern before interpreting the signed discrepancy as a sorting problem.
Subtract interior positions from total positions
Calling a mismatch proof of missing pieces
An excess often indicates sorting or dimensions, and a shortage can mean edge pieces remain in another pile. The stub cannot inspect the puzzle. Preserve the sign and investigate the model assumptions before making a replacement request or attributing the gap to a lost piece.
Inspect the relevant pile or layout
This puzzle-edge stub replaces a manual count or calculation, not source verification or the responsible person’s review.
Run it on the samples, right here
FIRST-LOAD
HYPOTHESIS / PROTOTYPE — checkout unavailable. Calculation is local. A draft is saved automatically in this browser profile when storage is available; Reset to sample clears it. Optional Pro history stores only five summaries and has its own deletion control. State links encode your inputs and can remain in browser history, clipboard or recipients’ records; share only non-sensitive rows. Optional external AI formatting leaves this device. The required site analytics beacon reports page activity; shared URLs contain encoded inputs. Do not treat an encoded URL as private. The calculator has no input-collection endpoint.
Rectangular-grid inventory arithmetic only. This does not detect lost pieces or certify a puzzle's completeness; confirm the actual cut layout and check sorting before contacting the maker about a replacement.
Data note: The puzzle-edge stub processes Puzzle code | columns of pieces | rows of pieces | sorted border count locally. Starter/sample selection and Run compute in this tab; no input is sent by the calculator. A local draft may be saved; explicit state-link sharing or optional external AI formatting can disclose inputs. Use non-sensitive labels.
Go deeper: the companion app files the same reading as a punched ticket stubs
The article demo above runs without limits. The companion app keeps a local history, exports the rows as CSV, prints the puzzle-edge stub reading, and holds your drafts on this device — one complete free app run; the proposed $4 one-time filing layer is not for sale.
The puzzle-edge stub answer stays complete for free. The proposed $4 one-time filing layer adds row CSV, print and five local reading summaries, not hidden answers. Checkout is unavailable; the article demo remains unlimited.
Rectangular-grid inventory arithmetic only. This does not detect lost pieces or certify a puzzle's completeness; confirm the actual cut layout and check sorting before contacting the maker about a replacement.
What this is built on
Method: Total positions are columns times rows. Interior positions are max(columns-2,0) times max(rows-2,0). Their difference is the modeled border. Subtract the observed edge-pile count for a signed discrepancy and use its absolute value for review. The summary adds those absolute values; a surplus and a shortage cannot cancel each other.
All sample records, dates, quantities and labels are invented. No outside policy, contract, rate, clock offset, measurement or accessibility standard is represented as verified.
Google’s official pricing documentation, fetched 2026-10-01, says AI Studio is free in available regions. Optional formatting may require a Google account; manual local entry requires none. Limits can change and free-tier content may be used to improve products. Do not send private records.
Before: a thin edge pile immediately meant a missing piece. After: grid dimensions, expected border and signed sorting discrepancy are separate observations.
Harbor's rectangular layout has 600 pieces and a border of 96: 600 minus the 28 × 18 interior. Its sorted edge pile has 92, a discrepancy of four. Orchard's 12 × 8 layout has 36 border pieces and its pile has 36, so its discrepancy is zero. The summary adds absolute discrepancies across the two independent puzzles; it does not claim four pieces are definitely missing.
A three-by-three grid has one interior position and eight border positions. A pile labeled border containing nine pieces exceeds the expected border by one, so the signed row gap is -1 and the absolute summary is one. This may be a sorting mistake, a mistaken layout or a nonstandard cut; the direction matters when deciding what to inspect.
Every piece in a one-column, seven-row rectangle lies on the border. The interior formula uses max(columns-2,0) × max(rows-2,0), giving no interior positions and seven border positions. A simple 2w+2h-4 perimeter formula would be wrong for this degenerate layout. The zero confirms the entered count under a rectangular-grid assumption, not the condition of every piece.
Optional AI formatting, never the calculation
Manual entry completes this puzzle-edge stub for free without signup. If available to you, the free AI Studio interface linked in the sources may format fictional or non-sensitive notes; external access may require an account. No API key or AI call is built into this tool. Free-tier content may be used to improve products. Review each cell and transcribe it to the labeled row schema; do not paste the JSON object into the row box.
Format only these fictional or non-sensitive notes for a puzzle-edge stub. Return strict JSON shaped as {"rows": [{"label": "string", "cells": ["string", "string", "string"]}], "setting": "string"}. The columns are Puzzle code | columns of pieces | rows of pieces | sorted border count; the setting is Reader-selected border discrepancy review mark (pieces). Keep all supplied strings and quantities exactly; do not calculate, infer missing entries, invent dates or add advice. If any required value is missing, return an empty rows array and ask me for it separately. I will verify every cell against my source and manually transcribe rows using vertical bars before running the local calculator.
An AI response is not executed, fetched or trusted as a result. Missing values remain questions; the strict local parser checks the rows you actually enter.