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🎲 Today's Puzzle Overview
August 19, 2025 — Pips day two, puzzles #4, #5, and #6. Rodolfo Kurchan returns for easy, and Heidi Erwin handles medium and hard again, building quickly on the patterns from day one.
The easy introduces a single-cell sum=0 region — a pip value of zero is the only valid answer — alongside a single-cell sum=6 that bookends the grid from the other end. Medium brings a four-cell equals region that spans the entire middle row, with a trio of constraints below it that chain together neatly.
The hard puzzle debuts a new region type: unequal. Three cells in the same unequal region must each hold a different pip value from one another — no two can match. Alongside that, a six-cell equals region winds through the center of the board, and a set of single-cell sums scatter across the grid to give you specific pip anchors to build from.
💡 Progressive Hints
Try these hints one at a time. Each hint becomes more specific to help you solve it yourself!
💡 Two solo sum regions sit at opposite ends of the grid
One cell at the top and one at the bottom each carry a single-cell sum constraint. Both tell you the exact pip value for free — no calculation needed. Start with either one and see where its domino partner lands.
💡 The bottom cell has the lowest possible target
A sum of zero means only one pip value is valid. The domino you place there has its other end land in the equals region — and that gives you both cells of the equals pair at once.
💡 Full answer
Sum=6 at [0,1] forces a 6 there — place [6–1] vertically with 6 at [0,1] and 1 at [1,1] (empty ✓). Sum=5 at [1,2] forces a 5 — place [5–3] vertically with 5 at [1,2] and 3 at [2,2] (empty ✓). Sum=0 at [3,1] forces a 0 — place [2–0] vertically with 2 at [2,1] and 0 at [3,1] ✓. The equals region at [2,0]–[2,1] needs both cells to match: [2,1]=2, so [2,0]=2. Last domino: [2–4] places 2 at [2,0] ✓ and 4 at [1,0] (empty). Puzzle complete.
💡 The equals row connects the top and bottom of the board
A four-cell equals region runs across the entire middle row. Figure out what single pip value can fill all four cells — the constraints above and below it narrow the options significantly.
💡 Start from the bottom corners and work toward the middle
The bottom row has two solo sum regions at [3,2] and [3,4]. Each hands you a specific pip value. One of those feeds directly into the three-cell sum region above it, and the other points straight to the equals row.
💡 Full answer
Sum=2 at [3,2] forces 2 — place [2–1] vertically with 2 at [3,2] and 1 at [2,2]. Sum=6 at [3,4] forces 6 — place [1–6] vertically with 1 at [3,3] and 6 at [3,4] ✓. Sum=3 at [2,2]+[2,3]+[3,3]: [2,2]=1 and [3,3]=1, so [2,3]=1. Place [1–0] horizontally with 1 at [2,3] ✓ and 0 at [2,4] (empty). Greater>3 at [0,3] needs 4 or more — place [3–4] vertically with 3 at [1,3] and 4 at [0,3] ✓. That anchors the equals row: [1,3]=3, so all four cells must be 3. Place [3–3] horizontally at [1,1]=3 and [1,2]=3. Place [1–3] vertically with 1 at [0,0] (empty ✓) and 3 at [1,0]. Equals row confirmed: 3=3=3=3 ✓.
💡 A new constraint type: unequal
The unequal region requires all three of its cells to hold different pip values — no two can match. Unlike equals, it doesn't tell you what values go there, only that they must all be distinct. Look at nearby constraints to narrow down the options.
💡 A two-cell sum=0 forces both cells to zero
The sum=0 region at the top of the grid covers two cells. Both must be zero — there's no other way to sum to nothing. Find the dominos that can place zeros in both spots, noting where their other ends land.
💡 A six-cell equals region winds through the center
Six cells spread across the middle of the board must all share the same pip value. The single-cell sums adjacent to the region tell you which specific value fills all six. Once that value is pinned, each of the six placements confirms one of the nearby single-cell sums.
💡 Single-cell sums are scattered across the grid — collect them first
Multiple isolated sum regions appear around the board, each giving away a free pip value. Gathering those anchors before tackling the equals region makes the whole puzzle fall into a clean sequence.
💡 Full answer
Sum=4 at [4,2]: place [4–1] horizontally with 4 at [4,2] and 1 at [4,3]. Sum=0 at [0,1]+[1,1]: place [0–4] horizontally with 0 at [0,1] and 4 at [0,0]; place [1–0] vertically with 1 at [2,1] and 0 at [1,1]. 0+0=0 ✓. The six-cell equals region has [2,1]=1 anchoring it — all six must be 1. Place [1–2] horizontally with 1 at [2,2] and 2 at [2,3] (sum=2 ✓). Place [3–1] vertically with 3 at [3,1] (sum=3 ✓) and 1 at [3,2]. Place [5–1] horizontally with 5 at [3,4] (sum=5 ✓) and 1 at [3,3]. [4,3]=1 already from the first step ✓. Place [6–1] horizontally with 6 at [4,5] (sum=6 ✓) and 1 at [4,4]. All six equals cells confirmed as 1 ✓. Unequal region [0,0],[1,0],[2,0]: [0,0]=4; place [5–6] vertically with 5 at [1,0] and 6 at [2,0]. 4≠5≠6 ✓. Sum=7 at [2,5]+[3,5]: place [3–4] vertically with 3 at [2,5] and 4 at [3,5]. 3+4=7 ✓. Puzzle complete.
🎨 Pips Solver
Aug 19, 2025
Click a domino to place it on the board. You can also click the board, and the correct domino will appear.
✅ Final Answer & Complete Solution For Hard Level
The key to solving today's hard puzzle was identifying the placement for the critical dominoes highlighted in the starting grid. Once those were in place, the rest of the puzzle could be solved logically. See the final grid below to compare your solution.
Starting Position & Key First Steps
This image shows the initial puzzle grid for the hard level, with a few critical first placements highlighted.
Final Answer: The Solved Grid for Hard Mode
Compare this final grid with your own solution to see the correct placement of all dominoes.
🔧 Step-by-Step Answer Walkthrough For Easy Level
1
Step 1: Top single-cell sum fixes the first placement
Cell [0,1] is a lone sum=6 region — it holds exactly 6. Place [6–1] vertically: 6 at [0,1] and 1 falling to [1,1] (empty).
2
Step 2: Middle single-cell sum fills column 2
Cell [1,2] is a lone sum=5 region — it holds exactly 5. Place [5–3] vertically: 5 at [1,2] and 3 at [2,2] (empty).
3
Step 3: Bottom single-cell sum triggers the equals region
Cell [3,1] is a lone sum=0 region — it holds exactly 0. Place [2–0] vertically: 2 at [2,1] and 0 at [3,1] ✓. The equals region at [2,0]–[2,1] now has [2,1]=2, so [2,0] must also be 2.
4
Step 4: Last domino seals the equals region
One domino remains: [2–4]. Its 2-end matches [2,0] perfectly (equals confirmed ✓) and its 4-end fills the last empty cell at [1,0]. Puzzle complete.
🔧 Step-by-Step Answer Walkthrough For Medium Level
1
Step 1: Two bottom-corner sums reveal the first two dominoes
Cell [3,2] is a lone sum=2 — place [2–1] vertically with 2 at [3,2] and 1 reaching up to [2,2]. Cell [3,4] is a lone sum=6 — place [1–6] vertically with 1 at [3,3] and 6 at [3,4] ✓.
2
Step 2: The three-cell sum region fills in from known values
The sum=3 region at [2,2]+[2,3]+[3,3] now has [2,2]=1 and [3,3]=1. The remaining cell [2,3] must be 1 to reach 3. Place [1–0] horizontally: 1 at [2,3] ✓ and 0 at [2,4] (empty).
3
Step 3: Greater-than constraint pins the equals row's value
Cell [0,3] needs a value greater than 3 — so 4 or more. Place [3–4] vertically: 3 at [1,3] and 4 at [0,3] ✓. That 3 at [1,3] anchors the four-cell equals row — all four cells in row 1 must be 3.
4
Step 4: Fill the equals row across row 1
Place [3–3] horizontally at [1,1]=3 and [1,2]=3. Place [1–3] vertically with 1 at [0,0] (empty ✓) and 3 at [1,0]. Equals check: [1,0]=[1,1]=[1,2]=[1,3]=3 ✓. Puzzle complete.
🔧 Step-by-Step Answer Walkthrough For Hard Level
1
Step 1: Single-cell sum=4 opens the bottom row
Cell [4,2] is a lone sum=4 region — it holds exactly 4. Place [4–1] horizontally: 4 at [4,2] and 1 at [4,3]. This 1 will become part of the six-cell equals region.
2
Step 2: Sum=0 pair forces two zeros into the top
The sum=0 region at [0,1] and [1,1] requires both cells to be 0. Place [0–4] horizontally: 0 at [0,1] and 4 at [0,0]. Place [1–0] vertically: 1 at [2,1] and 0 at [1,1]. Sum check: 0+0=0 ✓.
3
Step 3: The six-cell equals region is anchored at 1
The equals region covers [2,1],[2,2],[3,2],[3,3],[4,3],[4,4] — and [2,1]=1 from step 2, while [4,3]=1 from step 1. All six cells must be 1. Place [1–2] horizontally: 1 at [2,2] and 2 at [2,3] (sum=2 ✓).
4
Step 4: Continue filling the equals region downward
Place [3–1] vertically: 3 at [3,1] (sum=3 ✓) and 1 at [3,2]. Place [5–1] horizontally: 5 at [3,4] (sum=5 ✓) and 1 at [3,3]. Four of the six equals cells now confirmed.
5
Step 5: Close the equals region at the bottom
Place [6–1] horizontally: 6 at [4,5] (sum=6 ✓) and 1 at [4,4]. All six cells of the equals region now hold 1 ✓.
6
Step 6: Satisfy the unequal left column
The unequal region at [0,0],[1,0],[2,0] needs three distinct values. [0,0]=4 is already placed. Place [5–6] vertically: 5 at [1,0] and 6 at [2,0]. Check: 4≠5≠6 — all different ✓.
7
Step 7: Last placement wraps the sum-7 pair
One domino remains: [3–4]. The sum=7 region at [2,5]+[3,5] needs two cells totaling 7. Place [3–4] vertically: 3 at [2,5] and 4 at [3,5]. 3+4=7 ✓. Puzzle complete.
💡 Pro Tips for Similar Puzzles
Start with Constraints
Always begin with the most constrained regions - sum regions with small numbers or tight spaces.
Use Equal Regions
Use "equal" regions as anchors - they eliminate many possibilities quickly.
Work Systematically
Let the rules guide your placement rather than guessing randomly.
Double-Check
Verify each region's rules are satisfied before moving to the next.
💬 Community Discussion
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