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Hints for solving the September 16 Hard board
Start with the single-cell sum of 4
A region containing one cell with an exact sum of 4 fixes that cell at 4. Use this immediately to narrow the possible domino orientations around it.
Account for the doubles
The tray includes 2–2, 5–5, 4–4 and 0–0. If both halves of a double land inside the four-cell all-different region, that placement is impossible: the region cannot contain a repeated value. The double may still be usable elsewhere, where the region rules permit matching values.
Use sums as placement checks
As you place tiles, check complete regions against their clues. The solution includes 5 and 6 in the sum-11 region, three 5s in the sum-15 region, and 6, 4 and 4 in the sum-14 region. The less-than-5 singleton is a bound rather than an exact-sum clue; its value is 4.
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September 16 Pips Hard solution by region
These are the solved values in each constrained region. The all-different region has four cells; the other region sizes are shown in the listed values.
| Region clue | Values | Check |
|---|---|---|
| All different (4 cells) | 3, 2, 1, 5 | No value repeats |
| Sum 7 (3 cells) | 2, 2, 3 | 7 total |
| Sum 4 (1 cell) | 4 | 4 total |
| Sum 10 (2 cells) | 5, 5 | 10 total |
| Sum 11 (2 cells) | 5, 6 | 11 total |
| Sum 15 (3 cells) | 5, 5, 5 | 15 total |
| Less than 5 (1 cell) | 4 | 4 is below 5 |
| Sum 2 (4 cells) | 1, 1, 0, 0 | 2 total |
| Sum 14 (3 cells) | 6, 4, 4 | 14 total |
| Sum 4 (2 cells) | 2, 2 | 4 total |
| Sum 4 (1 cell) | 4 | 4 total |
Exact domino placements
Coordinates are counted from the top-left of the board, with row 1 and column 1 at the top-left. The first value listed for each tile is placed in the first coordinate; for a horizontal tile, the coordinates are given in the order specified, which may run right-to-left.
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- Place 2–4 horizontally: row 8, column 2 holds 2; row 8, column 1 holds 4.
- Place 5–6 vertically: row 2, column 8 holds 5; row 3, column 8 holds 6.
- Place 2–2 vertically: row 1, column 6 and row 2, column 6.
- Place 5–4 horizontally: row 1, column 8 holds 5; row 1, column 7 holds 4.
- Place 3–2 vertically: row 1, column 3 holds 3; row 2, column 3 holds 2.
- Place 5–5 horizontally across row 5, columns 2–3.
- Place 4–1 horizontally across row 5, columns 5–6.
- Place 5–2 vertically: row 6, column 2 holds 5; row 7, column 2 holds 2.
- Place 4–4 vertically: row 7, column 7 and row 8, column 7.
- Place 1–6 vertically: row 5, column 7 holds 1; row 6, column 7 holds 6.
- Place 5–3 horizontally: row 3, column 7 holds 5; row 3, column 6 holds 3.
- Place 0–0 horizontally across row 5, columns 8–9.
- Place 5–1 horizontally: row 3, column 4 holds 5; row 3, column 3 holds 1.
How to verify the completed board
Pips requires covering every board square with domino halves while obeying each region’s rule; each domino is used once. This Hard board has 26 squares, 13 dominoes and 11 constrained regions. After entering the placements, confirm that all 13 tiles are used and that the region values match the clues above. The date-specific solution pages credit Rodolfo Kurchan as Hard’s constructor and identify Ian Livengood as editor. Open NYT Pips.
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