Archive · Pips #45
Pips #45 (November 9, 2026): the three boards and their solutions
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Pips #45 is day 45 of Puzzlune Pips: three domino boards for Monday, November 9, 2026, Easy with 5 dominoes on a 5×3 grid, Medium with 7 dominoes on a 5×4 grid, Hard with 10 dominoes on a 6×5 grid. Every region on a board carries a rule, shown as a badge: a number means the pips inside add up to it, “=” means every pip is the same, “≠” means all different, and “<” or “>” compare the region's total to a number. Below, each board's regions are listed with what their rule demands, followed by the full placement.
Pips #45 in numbers
| Easy | 5×3 · 5 dominoes · 4 regions |
| Medium | 5×4 · 7 dominoes · 4 regions |
| Hard | 6×5 · 10 dominoes · 8 regions |
Easy: 5×3 board, 5 dominoes, 4 regions
The dominoes are 2–2, 3–4, 0–0, 5–0, 4–4: 24 pips over 10 cells. The 2 sum regions ask for 12 pips across 5 cells, so the remaining 5 cells share the other 12. 2 regions need every pip the same, which only doubles or matching halves of different dominoes can supply. This board accepts 2 valid arrangements; one is shown below.
| Region | Cells | Rule |
|---|---|---|
| 7 | 3 | adds up to 7 (average 2.3 per cell) |
| 5 | 2 | adds up to 5 (average 2.5 per cell) |
| = | 3 | all pips equal |
| = | 2 | all pips equal |
Easy board: the solution
Pip counts per cell; colours mark the regions, the small label is the region's rule.
Domino by domino: 2–2 down column 1, rows 2–3; 3–4 across row 2, columns 2–3; 0–0 down column 4, rows 2–3; 5–0 down column 5, rows 1–2; 4–4 across row 1, columns 3–4.
Medium: 5×4 board, 7 dominoes, 4 regions
The dominoes are 3–3, 4–4, 2–2, 5–5, 4–0, 6–4, 4–3: 49 pips over 14 cells. The 3 sum regions ask for 33 pips across 10 cells, so the remaining 4 cells share the other 16. 1 region needs every pip the same, which only doubles or matching halves of different dominoes can supply. The arrangement below is the unique answer.
| Region | Cells | Rule |
|---|---|---|
| 12 | 3 | adds up to 12 (average 4.0 per cell) |
| 14 | 4 | adds up to 14 (average 3.5 per cell) |
| = | 4 | all pips equal |
| 7 | 3 | adds up to 7 (average 2.3 per cell) |
Medium board: the solution
Pip counts per cell; colours mark the regions, the small label is the region's rule.
Domino by domino: 3–3 down column 5, rows 1–2; 4–4 across row 1, columns 1–2; 2–2 across row 4, columns 4–5; 5–5 across row 3, columns 1–2; 0–4 across row 2, columns 2–3; 4–6 across row 1, columns 3–4; 4–3 down column 3, rows 3–4.
Hard: 6×5 board, 10 dominoes, 8 regions
The dominoes are 0–0, 6–1, 6–2, 6–0, 4–6, 1–1, 0–3, 0–2, 5–5, 2–2: 52 pips over 20 cells. The 5 sum regions ask for 34 pips across 14 cells, so the remaining 6 cells share the other 18. 2 regions need every pip the same, which only doubles or matching halves of different dominoes can supply. This board accepts 8 valid arrangements; one is shown below.
| Region | Cells | Rule |
|---|---|---|
| 4 | 2 | adds up to 4 (average 2.0 per cell) |
| 13 | 4 | adds up to 13 (average 3.3 per cell) |
| <7 | 2 | total below 7 |
| 6 | 3 | adds up to 6 (average 2.0 per cell) |
| 1 | 3 | adds up to 1 (average 0.3 per cell) |
| 10 | 2 | adds up to 10 (average 5.0 per cell) |
| = | 2 | all pips equal |
| = | 2 | all pips equal |
Hard board: the solution
Pip counts per cell; colours mark the regions, the small label is the region's rule.
Domino by domino: 0–0 down column 6, rows 1–2; 6–1 across row 3, columns 5–6; 2–6 across row 1, columns 3–4; 6–0 across row 2, columns 4–5; 4–6 down column 2, rows 3–4; 1–1 down column 2, rows 1–2; 0–3 down column 4, rows 3–4; 2–0 down column 3, rows 2–3; 5–5 down column 3, rows 4–5; 2–2 down column 1, rows 3–4.
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