Shade Link practice: predict the counts and protect the connector.
Try a new fixed board, fill a three-count prediction ledger, and test an extra shade that splits a valid path into three groups. Reveal the full deductions and recovery steps after trying.
Can you predict all three check results before asking the game? This new challenge combines a row of three equal numbers with forced decisions across columns. Then it asks you to test an extra shade that creates no repeated pair or shaded side contact, yet breaks the remaining path. The printed numbers differ from both earlier lessons and every board in the seven-puzzle New collection. “Advanced” describes the tasks here, not a measured difficulty rating.
Try the new board first
Choose Practice this example beside the article, or Load advanced board in the game. Confirm Toggles 0 and these numbers. R means row and C means column, counted from the top left.
2 1 2 2 2 4 1 3 3 3 3 2 4 2 3 3
Keep only one unshaded copy of each number in any row or column. Shaded cells may meet at corners but cannot share sides. All unshaded cells must stay connected by horizontal and vertical steps. You need not keep every value from 1 to 4 in each line.
- Before any toggle, count equal-number pairs. Three equal numbers in one line create three pairs, not one. Enter your prediction in the three fields beneath the live board.
- Find two shades forced by the three consecutive threes in row 3. Predict the new counts before checking. Continue by considering the cells that must remain unshaded beside those shades.
- Find a complete answer. Before pressing Check shading, ask whether shading the four at R2C2 as well would break a rule. Predict which counter changes and why.
Check prediction compares your three entries with the current pattern. It adds no toggle, does not tell you a next move and does not register a win. Check shading is the separate rule test that finishes a correct board. Blank or fractional guesses are refused. Editing a cell or using Undo clears old comparison feedback; your entries remain for revision. Retry, loading another board or New puzzle also clears the entries.
Reveal the forced deductions and complete five-toggle route
In row 3, the three consecutive threes occupy C1, C2 and C3. At least two must be shaded to leave no repeated three. Three shades would share sides. Of the possible two-cell choices, only the two endpoints avoid a shared side. Therefore shade R3C1 and R3C3, keeping R3C2 unshaded. This argument depends on three equal numbers in consecutive cells; it is not a rule about any three numbers scattered across the grid.
R3C3 is shaded, so R4C3 must remain unshaded beside it. R4C3 is a three; its equal partner at R4C4 must therefore be shaded. Similarly, shaded R3C1 forces R2C1 to remain unshaded. That two forces its column partner R1C1 to be shaded. Finally, shaded R3C3 forces R3C4 to remain unshaded. Its two forces R1C4, the other two in column 4, to be shaded.
Retry for a clean comparison. Activate each listed cell once. You may Check prediction or Check shading between steps; neither adds a toggle. Every checkpoint below has 0 shaded side pairs and 1 unshaded group.
- Shade R3C1. Toggles 1; 9 equal-number pairs.
- Shade R3C3. Toggles 2; 7 pairs.
- Shade R4C4. Toggles 3; 5 pairs.
- Shade R1C1. Toggles 4; 2 pairs.
- Shade R1C4. Toggles 5; 0 pairs.
X 1 2 X 2 4 1 3 X 3 X 2 4 2 3 X
The remaining row lists are (1, 2), (2, 4, 1, 3), (3, 2) and (4, 2, 3). The column lists are (2, 4), (1, 4, 3, 2), (2, 1, 3) and (3, 2). No list repeats a number. Five shaded cells share no sides, and the eleven unshaded cells form one group. Independent checking of every possible shading pattern finds exactly one answer for these numbers.
Stop before Check shading if you want to run the connector experiment next. A matching prediction leaves the game editable, even at the correct pattern. If you already registered the win, Retry and replay the five shades so you can test the extra cell.
Keep a three-count ledger
Write down a forecast before revealing each result. On the live board, enter it into Predict equal-number pairs, Predict shaded side pairs and Predict unshaded groups. The fields compare with the board as it stands, so load or replay the specified checkpoint first.
Reveal the count ledger and explain the initial eleven pairs
In this ledger, Pairs means equal-number pairs, Sides means shaded side pairs and Groups means unshaded groups.
| Checkpoint | Pairs | Sides | Groups |
|---|---|---|---|
| No shades; Toggles 0 | 11 | 0 | 1 |
| R3C1 and R3C3; Toggles 2 | 7 | 0 | 1 |
| All five answer shades; Toggles 5 | 0 | 0 | 1 |
| Those five plus R2C2; Toggles 6 | 0 | 0 | 3 |
At the start, row 1 has three twos, contributing 3 pairs; row 3 has three threes, contributing 3; row 4 has two threes, contributing 1. Column 1 contributes 1 pair of twos, column 3 contributes 1 pair of threes, and column 4 contributes a pair of twos and a pair of threes. The total is 3 + 3 + 1 + 1 + 1 + 2 = 11. All other rows and columns contribute zero.
Removing R3C1 deletes its two row pairs. Removing R3C3 then deletes the remaining row-3 pair and its column-3 pair. The count falls from 11 to 9 to 7. An edit need not remove exactly one pair, and a lower pair count does not prove that the two other rules still hold. Count each pair of cells in a shared row or column once; do not count a repeated value in unrelated lines.
For an incorrect prediction, try 1, 0, 1 on the five-shade answer. The comparison reports the actual 0, 0, 1 while leaving Toggles 5 and the board editable. Revise the first entry to zero and compare again. Only Check shading registers the solved state and locks the board.
Test a connector, not just a duplicate
On the five-shade pattern before the win is registered, shade R2C2 as a sixth toggle. Its four has no equal unshaded partner in its row or column. None of its side neighbours is shaded. Does that make the extra shade harmless? Predict the three counts before opening the last answer.
Reveal the three groups, recovery and final self-check
The result is Toggles 6: 0 equal-number pairs, 0 shaded side pairs and 3 unshaded groups. The ten remaining unshaded cells split into these sets:
- {R1C2, R1C3, R2C3, R2C4, R3C4}
- {R2C1}
- {R3C2, R4C1, R4C2, R4C3}
R2C2 was the connector between the isolated left cell, the upper-right path and the lower path. Once it is shaded, diagonal contact between those sets does not join them. The extra shade does not introduce a duplicate or touch another shade by a side; it violates connectivity alone. This is a statement about this specific pattern, not a rule that every number with no duplicates must always remain unshaded on every puzzle.
Check prediction can confirm 0, 0, 3 without finishing or editing. Check shading gives the rule failure and also adds no toggle. Undo once removes only R2C2, returning to Toggles 5, the five-shade answer and 0, 0, 1. Comparison feedback clears. Press Check shading to finish. A successful check locks all sixteen number buttons and moves focus to Undo last toggle.
Predict one more recovery: Undo after that win removes the latest retained answer toggle, R1C4. You return to Toggles 4 with R1C1, R3C1, R3C3 and R4C4 shaded. A check reports 2 equal-number pairs, 0 shaded side pairs and 1 unshaded group. The two pairs are R1C3 with R1C4 and R1C4 with R3C4. Shade R1C4 again and Check to finish. Retry instead clears the whole attempt, including predictions, with the numbers unchanged.
What this exercise does and does not establish
The consecutive-triple deduction solves part of this board; forced unshaded neighbours carry the reasoning across lines. The connector experiment checks a separate global condition. These techniques do not guarantee a short deduction route for every larger puzzle, and a correct prediction is not a proof that your next choice permits a complete answer.
Load advanced board restores this exact new teaching arrangement. It is an extra fixed exercise outside the unchanged seven-board New collection, not a new game. New puzzle clears the practice address and returns to that collection. Refreshing the advanced practice address restores these numbers with no saved moves or predictions. The comparison fields are local to this browser tab, with no account, payment, timer, network submission or advertisement action.