Archive · Pips #21
Pips #21 (October 16, 2026): the three boards and their solutions
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Pips #21 is day 21 of Puzzlune Pips: three domino boards for Friday, October 16, 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 8×4 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 #21 in numbers
| Easy | 4×4 · 5 dominoes · 4 regions |
| Medium | 5×4 · 7 dominoes · 5 regions |
| Hard | 8×4 · 10 dominoes · 8 regions |
Easy: 4×4 board, 5 dominoes, 4 regions
The dominoes are 2–2, 4–6, 6–6, 2–5, 4–3: 40 pips over 10 cells. The 3 sum regions ask for 34 pips across 7 cells, so the remaining 3 cells share the other 6. 1 region needs 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 |
|---|---|---|
| 12 | 2 | adds up to 12 (average 6.0 per cell) |
| = | 3 | all pips equal |
| 7 | 2 | adds up to 7 (average 3.5 per cell) |
| 15 | 3 | adds up to 15 (average 5.0 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 across row 1, columns 1–2; 4–6 across row 4, columns 1–2; 6–6 down column 3, rows 3–4; 2–5 down column 2, rows 2–3; 4–3 across row 2, columns 3–4.
Medium: 5×4 board, 7 dominoes, 5 regions
The dominoes are 4–4, 0–0, 4–1, 2–2, 6–2, 5–5, 6–0: 41 pips over 14 cells. The 3 sum regions ask for 22 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 |
|---|---|---|
| = | 3 | all pips equal |
| 4 | 3 | adds up to 4 (average 1.3 per cell) |
| >12 | 3 | total above 12 |
| 13 | 3 | adds up to 13 (average 4.3 per cell) |
| 5 | 2 | adds up to 5 (average 2.5 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: 4–4 across row 1, columns 2–3; 0–0 across row 2, columns 4–5; 1–4 across row 3, columns 4–5; 2–2 across row 4, columns 1–2; 6–2 down column 3, rows 3–4; 5–5 across row 2, columns 1–2; 0–6 across row 3, columns 1–2.
Hard: 8×4 board, 10 dominoes, 8 regions
The dominoes are 6–0, 3–3, 3–2, 2–6, 4–6, 2–2, 6–5, 5–0, 4–3, 4–1: 67 pips over 20 cells. The 6 sum regions ask for 54 pips across 15 cells, so the remaining 5 cells share the other 13. 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 |
|---|---|---|
| 11 | 4 | adds up to 11 (average 2.8 per cell) |
| 10 | 2 | adds up to 10 (average 5.0 per cell) |
| 6 | 2 | adds up to 6 (average 3.0 per cell) |
| = | 2 | all pips equal |
| 10 | 3 | adds up to 10 (average 3.3 per cell) |
| 6 | 2 | adds up to 6 (average 3.0 per cell) |
| 11 | 2 | adds up to 11 (average 5.5 per cell) |
| = | 3 | 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: 6–0 across row 2, columns 1–2; 3–3 across row 4, columns 1–2; 3–2 across row 3, columns 2–3; 2–6 across row 4, columns 3–4; 4–6 across row 3, columns 4–5; 2–2 across row 4, columns 5–6; 6–5 across row 1, columns 7–8; 5–0 down column 6, rows 1–2; 4–3 across row 3, columns 6–7; 4–1 across row 2, columns 7–8.
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