Pips answers for Monday, July 13, 2026

Start with the “<1” region at the center: the only way to make it with these dominoes is 0 + 0 + 0.

• the “=” region at the left: 2, 2
• the 6 region at the center: 1, 5
• the “<1” region at the center: 0, 0, 0
• the single-cell “>3” region at the right: 5
• the single-cell 3 region at the bottom: 3

1. The “<1” region at the center must total less than 1 — nothing else fits. Place the 0–3 domino vertically on row 3, column 3 and row 4, column 3.
2. Row 3, column 4 has only one open neighbor, so its domino must run to row 3, column 5; the “<1” region at the center must total less than 1 (1 of its 3 cells is already filled) — nothing else fits. Place the 0–5 domino horizontally on row 3, column 4 and row 3, column 5.
3. The “=” region at the left needs every pip to match — nothing else fits. Place the 0–2 domino horizontally on row 3, column 1 and row 3, column 2.
4. Row 2, column 1 has only one open neighbor, so its domino must run to row 2, column 2; the “=” region at the left needs every pip to match (1 of its 2 cells is already filled) — nothing else fits. Place the 1–2 domino horizontally on row 2, column 1 and row 2, column 2.
5. Row 2, column 3 has only one open neighbor, so its domino must run to row 1, column 3; the 6 region at the center needs a total of exactly 6 (1 of its 2 cells is already filled) — nothing else fits. Place the 3–5 domino vertically on row 1, column 3 and row 2, column 3.

Start with the 2 region at the center: only 0 + 0 + 2, or 0 + 1 + 1 can make it with these dominoes.

• the “=” region at the top-left: 5, 5
• the 4 region at the top: 1, 3
• the 2 region at the center: 0, 0, 2
• the “=” region at the left: 4, 4
• the 3 region at the bottom: 1, 2
• the single-cell 6 region at the bottom: 6

1. The 3 region at the bottom needs a total of exactly 3 — nothing else fits. Place the 1–6 domino horizontally on row 5, column 2 and row 5, column 3.
2. The 2 region at the center needs a total of exactly 2 — nothing else fits. Place the 0–0 domino vertically on row 3, column 3 and row 4, column 3.
3. The 2 region at the center needs a total of exactly 2 (2 of its 3 cells are already filled) — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 2–5 domino horizontally on row 2, column 3 and row 2, column 4.
4. The “=” region at the top-left needs every pip to match — nothing else fits. Place the 5–5 domino vertically on row 1, column 1 and row 2, column 1.
5. The “=” region at the left needs every pip to match — nothing else fits. Place the 2–4 domino vertically on row 3, column 2 and row 4, column 2.
6. Row 3, column 1 has only one open neighbor, so its domino must run to row 4, column 1; the “=” region at the left needs every pip to match (1 of its 2 cells is already filled) — nothing else fits. Place the 1–4 domino vertically on row 3, column 1 and row 4, column 1.
7. Row 1, column 2 has only one open neighbor, so its domino must run to row 1, column 3; the 4 region at the top needs a total of exactly 4 — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 1–3 domino horizontally on row 1, column 2 and row 1, column 3.

This board has more than one valid layout; the steps follow the official answer.

Start with the 3 region at the top: only 0 + 3, or 1 + 2 can make it with these dominoes.

• the 4 region at the top-left: 2, 2
• the 3 region at the top: 1, 2
• the single-cell “<2” region at the top: 0
• the 8 region at the top-right: 2, 6
• the “=” region at the top-right: 4, 4, 4
• the 3 region at the top-left: 0, 3
• the “=” region at the right: 5, 5
• the 5 region at the bottom-left: 1, 4
• the 4 region at the bottom-right: 2, 2
• the “=” region at the bottom-right: 3, 3
• the single-cell 5 region at the bottom-left: 5
• the single-cell 5 region at the bottom-right: 5

1. The 3 region at the top needs a total of exactly 3 — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 0–2 domino horizontally on row 1, column 4 and row 1, column 5.
2. The 3 region at the top needs a total of exactly 3 (1 of its 2 cells is already filled) — nothing else fits. Place the 1–3 domino vertically on row 1, column 3 and row 2, column 3.
3. Row 3, column 3 has only one open neighbor, so its domino must run to row 4, column 3; the 3 region at the top-left needs a total of exactly 3 (1 of its 2 cells is already filled) — nothing else fits. Place the 0–4 domino vertically on row 3, column 3 and row 4, column 3.
4. Row 1, column 1 has only one open neighbor, so its domino must run to row 1, column 2; the 4 region at the top-left needs a total of exactly 4 — nothing else fits. Place the 2–2 domino horizontally on row 1, column 1 and row 1, column 2.
5. Row 5, column 3 has only one open neighbor, so its domino must run to row 6, column 3; the 5 region at the bottom-left needs a total of exactly 5 (1 of its 2 cells is already filled) — nothing else fits. Place the 1–5 domino vertically on row 5, column 3 and row 6, column 3.
6. The “=” region at the bottom-right needs every pip to match — 4 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 3–5 domino horizontally on row 6, column 7 and row 6, column 8.
7. The 4 region at the bottom-right needs a total of exactly 4 — nothing else fits. Place the 2–3 domino horizontally on row 5, column 7 and row 5, column 8.
8. The “=” region at the right needs every pip to match — 3 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 2–5 domino horizontally on row 4, column 7 and row 4, column 8.
9. The “=” region at the top-right needs every pip to match — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 4–5 domino horizontally on row 3, column 7 and row 3, column 8.
10. The “=” region at the top-right needs every pip to match (1 of its 3 cells is already filled) — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 4–4 domino vertically on row 1, column 8 and row 2, column 8.
11. Row 1, column 7 has only one open neighbor, so its domino must run to row 2, column 7; the 8 region at the top-right needs a total of exactly 8 — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 2–6 domino vertically on row 1, column 7 and row 2, column 7.

This board has more than one valid layout; the steps follow the official answer.