Archive · Pips #20
Pips #20 (October 15, 2026): the three boards and their solutions
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Pips #20 is day 20 of Puzzlune Pips: three domino boards for Thursday, October 15, 2026, Easy with 5 dominoes on a 4×4 grid, Medium with 7 dominoes on a 5×4 grid, Hard with 10 dominoes on a 7×4 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 #20 in numbers
| Easy | 4×4 · 5 dominoes · 4 regions |
| Medium | 5×4 · 7 dominoes · 5 regions |
| Hard | 7×4 · 10 dominoes · 8 regions |
Easy: 4×4 board, 5 dominoes, 4 regions
The dominoes are 2–2, 2–4, 3–3, 1–3, 0–3: 23 pips over 10 cells. The 2 sum regions ask for 7 pips across 4 cells, so the remaining 6 cells share the other 16. 2 regions need every pip the same, which only doubles or matching halves of different dominoes can supply. This board accepts 4 valid arrangements; one is shown below.
| Region | Cells | Rule |
|---|---|---|
| = | 2 | all pips equal |
| = | 4 | all pips equal |
| 1 | 2 | adds up to 1 (average 0.5 per cell) |
| 6 | 2 | adds up to 6 (average 3.0 per cell) |
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 3–4; 2–4 across row 3, columns 2–3; 3–3 down column 4, rows 3–4; 1–3 across row 1, columns 3–4; 0–3 across row 2, columns 3–4.
Medium: 5×4 board, 7 dominoes, 5 regions
The dominoes are 0–2, 6–1, 2–3, 4–3, 5–5, 4–4, 2–4: 45 pips over 14 cells. The 3 sum regions ask for 26 pips across 8 cells, so the remaining 6 cells share the other 19. 1 region needs 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 |
|---|---|---|
| 14 | 4 | adds up to 14 (average 3.5 per cell) |
| <6 | 2 | total below 6 |
| 9 | 2 | adds up to 9 (average 4.5 per cell) |
| = | 4 | all pips equal |
| 3 | 2 | adds up to 3 (average 1.5 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: 0–2 across row 3, columns 4–5; 6–1 across row 2, columns 4–5; 2–3 across row 1, columns 3–4; 4–3 across row 4, columns 3–4; 5–5 across row 2, columns 1–2; 4–4 across row 3, columns 1–2; 2–4 down column 3, rows 2–3.
Hard: 7×4 board, 10 dominoes, 8 regions
The dominoes are 1–1, 6–6, 3–0, 4–1, 0–6, 1–2, 5–3, 2–2, 0–4, 4–4: 55 pips over 20 cells. The 4 sum regions ask for 26 pips across 9 cells, so the remaining 11 cells share the other 29. 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 |
|---|---|---|
| = | 3 | all pips equal |
| <8 | 2 | total below 8 |
| 7 | 3 | adds up to 7 (average 2.3 per cell) |
| 12 | 2 | adds up to 12 (average 6.0 per cell) |
| <9 | 3 | total below 9 |
| = | 3 | all pips equal |
| 4 | 2 | adds up to 4 (average 2.0 per cell) |
| 3 | 2 | adds up to 3 (average 1.5 per cell) |
Hard board: the solution
Pip counts per cell; colours mark the regions, the small label is the region's rule.
Domino by domino: 1–1 down column 3, rows 1–2; 6–6 across row 1, columns 5–6; 3–0 down column 2, rows 2–3; 4–1 down column 1, rows 3–4; 0–6 across row 4, columns 2–3; 1–2 across row 3, columns 3–4; 5–3 across row 2, columns 4–5; 2–2 across row 4, columns 4–5; 0–4 across row 3, columns 5–6; 4–4 across row 4, columns 6–7.
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