The Suspended Weave

Black out the boxes of this grid 12 × 12 to satisfy all series.

This page contains the solution.

The answer

The grid below is the only solution; ■ = black, · = empty.

Coordinates: lines from top to bottom, columns from left to right.
L / C	1	2	3	4	5	6	7	8	9	10	11	12
1	■	■	·	·	·	■	■	·	■	·	·	■
2	·	·	■	·	·	■	·	·	■	·	·	■
3	·	■	■	■	■	·	·	·	·	■	·	■
4	■	■	·	·	·	■	■	■	·	■	■	■
5	■	■	·	■	■	·	■	■	·	·	·	·
6	■	■	■	·	·	■	·	·	■	■	·	·
7	■	■	■	■	·	·	■	·	■	·	·	·
8	■	■	■	■	·	·	·	·	·	■	·	■
9	·	■	■	■	■	·	■	·	·	·	■	■
10	·	·	·	·	·	·	■	·	·	■	■	·
11	■	■	■	■	■	·	■	■	·	·	■	·
12	■	■	■	·	·	·	·	■	·	■	·	·

The reasoning

Start by listing the investments in each series. Keep only those compatible with the already fixed crosses: any box common to all investments can be fixed.
This intersecting closure is not enough here. Case analyses should be conducted on a line or column, each choice should be passed on to the perpendicular lines and a choice should be rejected as soon as a series can no longer be placed.
The exhaustive control visited 14 states, encountered 8 contradictions and reached 5 levels of assumptions. These measures describe this solver; they do not represent a universal ranking of players.
L4: 10 compatible placements; L4C6 black, L4C10 black.
L9: 20 compatible placements. L9C4 is filled.
L11: 10 compatible placements; Black L11C3, Black L11C4, Black L11C5.
C1: 10 compatible placements; black L5C1, black L6C1, black L7C1.
C2: 1 compatible placements; black L1C2, empty L2C2, black L3C2, black L4C2, black L5C2, black L6C2, black L7C2, black L8C2, black L9C2, black L10C2, empty L11C2, black L12C2.
C3: 9 compatible placements; L6C3 black, L7C3 black.
C4: 6 compatible placements; L6C4 empty, L7C4 black, L8C4 black, L10C4 empty, L12C4 empty.
C5: 35 compatible placements; L10C5 empty, L12C5 empty.
C7: 15 compatible placements. L10C7 is filled.
C10: 11 compatible placements. L5C10 is empty.
L3: 25 compatible placements; L3C3 black, L3C4 black.
L5: 8 compatible placements. L5C3 is empty.
L7: 15 compatible placements. L7C5 is empty.
L8: 25 compatible placements. L8C3 is filled.
L9: 16 compatible placements. L9C3 is filled.
L12: 15 compatible placements; black L12C1, black L12C3.
C1: 6 compatible placements; L10C1 empty, L11C1 black.
C3: 2 compatible placements; L1C3 empty, L10C3 empty.
C4: 2 compatible placements; L2C4 empty, L4C4 empty.
L1: 20 compatible placements. L1C1 is filled.
L4: 6 compatible placements; L4C7 black, L4C11 black.
L10: 3 compatible placements; L10C6 empty, L10C8 empty.
L11: 6 compatible placements. L11C6 is empty.
C1: 3 compatible placements. L2C1 is empty.
Case analysis on C3 : placement 1/2 = * * * * * * * * * * *
L4: 3 compatible placements. L4C1 is filled.
C1: 2 compatible placements. L9C1 is empty.
L9: 6 compatible placements; L9C5 black, L9C6 empty.
C5: 10 compatible placements. L8C5 is empty.
L8: 15 compatible placements. L8C1 is filled.
C1: 1 compatible placements. L3C1 is empty.
L3: 10 compatible placements; L3C5 black, L3C6 empty.
C5: 3 compatible placements; L2C5 empty, L4C5 empty.
L4: 1 compatible placements; L4C8 black, L4C9 empty, L4C12 black.
Case analysis on C4 : placement 2/2 = * * * * * * * * * * *
L5: 3 compatible placements; L5C5 black, L5C6 empty.
C5: 1 compatible investments; L1C5 empty, L6C5 empty.
C6: 4 compatible placements; L1C6 black, L2C6 black.
L1: 3 compatible placements; L1C7 black, L1C8 empty.
L2: 6 compatible placements. L2C7 is empty.
C8: 7 compatible placements. L2C8 is empty.
Case analysis on L1: placement 2/3 = ■·····················································································································································································································································································································
C9: 7 compatible placements; L2C9 black, L3C9 empty.
C10: 1 compatible placements; L2C10 empty, L3C10 black, L6C10 black, L7C10 empty, L8C10 black, L9C10 empty, L10C10 black, L11C10 empty, L12C10 black.
C11: 6 compatible placements. L3C11 is empty.
C12: 6 compatible placements; L2C12 black, L3C12 black, L5C12 empty.
L2: 1 compatible placements. L2C11 is empty.
L3: 1 compatible placements; L3C7 empty, L3C8 empty.
L5: 2 compatible placements; L5C8 black, L5C11 empty.
L6: 5 compatible placements. L6C12 is empty.
L8: 4 compatible placements; L8C9 empty, L8C11 empty.
L9: 3 compatible placements; L9C11 black, L9C12 black.
L10: 2 compatible placements. L10C12 is empty.
L11: 4 compatible placements. L11C8 is filled.
L12: 4 compatible placements; L12C9 empty, L12C11 empty.
C7: 3 compatible placements; L5C7 black, L6C7 empty, L11C7 black.
C8: 1 compatible placements; L6C8 empty, L7C8 empty, L8C8 empty, L9C8 empty, L12C8 black.
C11: 1 compatible placements; L6C11 empty, L7C11 empty, L10C11 black, L11C11 black.
C12: 1 compatible placements; L7C12 empty, L8C12 black, L11C12 empty, L12C12 empty.
L5: 1 compatible placements. L5C9 is empty.
L6: 1 compatible placements; L6C6 black, L6C9 black.
L7: 2 compatible placements. L7C9 is filled.
L8: 1 compatible placements; L8C6 empty, L8C7 empty.
L10: 1 compatible placements. L10C9 is empty.
L11: 1 compatible placements. L11C9 is empty.
L12: 1 compatible placements; L12C6 empty, L12C7 empty.
C6: 1 compatible placements. L7C6 is empty.
C7: 1 compatible placements; L7C7 black, L9C7 black.
C9: 1 compatible placements. L9C9 is empty.
Examples of contradictions encountered:
C10 has no legal placement left at depth 2.
L9 has no legal placement left at depth 3.
C10 has no legal placement left at depth 4.
C12 has no legal placement left at depth 5.
L7 has no legal placement left at depth 5.
C7 has no legal placement left at depth 5.
L7 has no legal placement left at depth 4.
L1 has no legal placement left at depth 1.

Common mistakes and false leads

Do not confuse an unknown box with an empty proven box.
A hypothesis must be cancelled with all its consequences if a series becomes impossible.
The form suggested by the first black boxes is not evidence.

How we verified this answer

Enumeration of placements by line, propagation by intersections and exhaustive search for up to two solutions; new verification of response series.

{
  "nodes": 14,
  "contradictions": 8,
  "depth": 5,
  "forced_cells": 375,
  "branches": 5
}

The simple intersection blocks; the crosses require an analysis of nested cases (depth 5, 8 branches impossible in the solver). Editorial level based on this need for coordination, not on the only format of the grid.

← Return to puzzle SOLO-022

L / C	1	2	3	4	5	6	7	8	9	10	11	12
1	■	■	·	·	·	■	■	·	■	·	·	■
2	·	·	■	·	·	■	·	·	■	·	·	■
3	·	■	■	■	■	·	·	·	·	■	·	■
4	■	■	·	·	·	■	■	■	·	■	■	■
5	■	■	·	■	■	·	■	■	·	·	·	·
6	■	■	■	·	·	■	·	·	■	■	·	·
7	■	■	■	■	·	·	■	·	■	·	·	·
8	■	■	■	■	·	·	·	·	·	■	·	■
9	·	■	■	■	■	·	■	·	·	·	■	■
10	·	·	·	·	·	·	■	·	·	■	■	·
11	■	■	■	■	■	·	■	■	·	·	■	·
12	■	■	■	·	·	·	·	■	·	■	·	·

L / C	1	2	3	4	5	6	7	8	9	10	11	12
1	■	■	·	·	·	■	■	·	■	·	·	■
2	·	·	■	·	·	■	·	·	■	·	·	■
3	·	■	■	■	■	·	·	·	·	■	·	■
4	■	■	·	·	·	■	■	■	·	■	■	■
5	■	■	·	■	■	·	■	■	·	·	·	·
6	■	■	■	·	·	■	·	·	■	■	·	·
7	■	■	■	■	·	·	■	·	■	·	·	·
8	■	■	■	■	·	·	·	·	·	■	·	■
9	·	■	■	■	■	·	■	·	·	·	■	■
10	·	·	·	·	·	·	■	·	·	■	■	·
11	■	■	■	■	■	·	■	■	·	·	■	·
12	■	■	■	·	·	·	·	■	·	■	·	·

L / C	1	2	3	4	5	6	7	8	9	10	11	12
1	■	■	·	·	·	■	■	·	■	·	·	■
2	·	·	■	·	·	■	·	·	■	·	·	■
3	·	■	■	■	■	·	·	·	·	■	·	■
4	■	■	·	·	·	■	■	■	·	■	■	■
5	■	■	·	■	■	·	■	■	·	·	·	·
6	■	■	■	·	·	■	·	·	■	■	·	·
7	■	■	■	■	·	·	■	·	■	·	·	·
8	■	■	■	■	·	·	·	·	·	■	·	■
9	·	■	■	■	■	·	■	·	·	·	■	■
10	·	·	·	·	·	·	■	·	·	■	■	·
11	■	■	■	■	■	·	■	■	·	·	■	·
12	■	■	■	·	·	·	·	■	·	■	·	·