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Archive · Pips #31

Pips #31 (October 26, 2026): the three boards and their solutions

Easy, Medium and Hard from Monday, October 26, 2026. Play them first; each board's answer is folded below. Replays don't affect your streak.

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Pips #31 is day 31 of Puzzlune Pips: three domino boards for Monday, October 26, 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 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 #31 in numbers

Easy4×4 · 5 dominoes · 4 regions
Medium5×4 · 7 dominoes · 4 regions
Hard6×5 · 10 dominoes · 8 regions

Easy: 4×4 board, 5 dominoes, 4 regions

The dominoes are 3–3, 6–6, 1–1, 4–4, 1–3: 32 pips over 10 cells. The 2 sum regions ask for 23 pips across 5 cells, so the remaining 5 cells share the other 9. 2 regions need every pip the same, which only doubles or matching halves of different dominoes can supply. This board accepts 3 valid arrangements; one is shown below.

RegionCellsRule
=2all pips equal
113adds up to 11 (average 3.7 per cell)
122adds up to 12 (average 6.0 per cell)
=3all 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: 3–3 across row 4, columns 2–3; 6–6 across row 2, columns 1–2; 1–1 across row 1, columns 3–4; 4–4 down column 3, rows 2–3; 1–3 down column 4, rows 2–3.

Medium: 5×4 board, 7 dominoes, 4 regions

The dominoes are 0–0, 3–3, 5–5, 0–5, 1–5, 1–2, 3–5: 38 pips over 14 cells. The 2 sum regions ask for 13 pips across 7 cells, so the remaining 7 cells share the other 25. 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.

RegionCellsRule
124adds up to 12 (average 3.0 per cell)
=3all pips equal
13adds up to 1 (average 0.3 per cell)
>134total above 13
Medium 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 2, rows 1–2; 3–3 across row 1, columns 4–5; 5–5 across row 3, columns 1–2; 0–5 down column 5, rows 3–4; 1–5 down column 3, rows 2–3; 1–2 across row 4, columns 3–4; 3–5 down column 4, rows 2–3.

Hard: 6×5 board, 10 dominoes, 8 regions

The dominoes are 0–3, 6–6, 4–4, 1–2, 2–6, 5–6, 0–4, 1–1, 1–3, 1–5: 61 pips over 20 cells. The 5 sum regions ask for 47 pips across 12 cells, so the remaining 8 cells share the other 14. 1 region needs 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.

RegionCellsRule
=3all pips equal
32adds up to 3 (average 1.5 per cell)
93adds up to 9 (average 3.0 per cell)
153adds up to 15 (average 5.0 per cell)
102adds up to 10 (average 5.0 per cell)
>62total above 6
<43total below 4
102adds up to 10 (average 5.0 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: 0–3 down column 6, rows 1–2; 6–6 down column 3, rows 1–2; 4–4 down column 2, rows 2–3; 1–2 across row 4, columns 1–2; 6–2 across row 5, columns 4–5; 5–6 down column 6, rows 4–5; 0–4 down column 3, rows 4–5; 1–1 across row 3, columns 3–4; 3–1 across row 2, columns 4–5; 1–5 down column 5, rows 3–4.

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