📑 Table of Contents
🎲 What is Pips?
Pips is a daily domino logic puzzle published by the New York Times. It combines elements of Sudoku and domino placement, challenging you to fill an irregular grid with dominoes while satisfying multiple constraints.
Each puzzle features a unique board shape with colored regions, each having a target sum. Your goal is to place all dominoes so that the numbers in each region add up to the target, while also respecting constraint symbols between adjacent cells.
The name "Pips" refers to the dots on dominoes (and dice). In this puzzle, you're working with pip values ranging from 0 to 6.
🎯 Understanding the Game Board
The Pips board is an irregular grid—not all cells are active. Some positions are "holes" that cannot be filled. The active cells form the puzzle area where you'll place dominoes.
Board Elements
- Active Cells: These are the positions where you can place domino halves. They're usually shown with a lighter background.
- Inactive Cells: These are blocked positions (holes) that cannot be used. They're typically darker or marked differently.
- Regions: Groups of connected active cells, each with a target sum. Regions are color-coded for easy identification.
- Constraints: Symbols (=, ≠, >, <) between adjacent cells that define relationships between their values.
Imagine a 4×4 grid where the top-left 2×2 area forms one region with target sum 10, and the bottom-right 2×2 area forms another region with target sum 8. The cells might have constraints like "=" between two adjacent cells, meaning they must have the same number.
🔗 Constraint Symbols Explained
Constraints are the key to solving Pips puzzles. They appear between adjacent cells and define mathematical relationships between the values in those cells.
Constraints apply to the final values in cells, not to the dominoes themselves. A single domino might have values [3,5], and when placed, the 3 and 5 go into different cells—each cell's value must satisfy its own constraints.
🀄 How Dominoes Work
In Pips, dominoes are the tools you use to fill the board. Each domino has two halves, each with a pip value from 0 to 6.
Domino Placement Rules
- Two Halves: Each domino covers exactly two adjacent cells (horizontally or vertically).
- No Overlap: Dominoes cannot overlap each other or extend outside the active grid.
- All Placed: Every domino must be placed—you cannot skip or remove dominoes once the puzzle starts.
- Fixed Set: The puzzle provides a specific set of dominoes. You cannot create new ones.
Pay attention to the domino inventory! If you only have one domino with a 6, and there's a single-cell region with target sum 6, that domino must go there.
🎨 Understanding Regions
Regions are groups of connected cells, each with a target sum shown in the top-left corner. All cells in a region must sum to this target.
Region Types
- Single-Cell Regions: The simplest—the cell's value must exactly equal the target. If target is 5, the cell must be 5.
- Multi-Cell Regions: The sum of all cells in the region must equal the target. A 3-cell region with target 12 could be 4+4+4, 3+4+5, etc.
- Equals Regions: When combined with "=" constraints, all cells in the region must have the same value. A 4-cell equals region with target 8 means all cells are 2.
Consider a 2-cell region with target sum 7. Possible combinations: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1. If one cell has a ">" constraint with value 4, then the other cell must be less than 4, so the only valid combination is 4+3 (with 4 > 3).
📝 Step-by-Step Solving Guide
Follow this systematic approach to solve any Pips puzzle:
Step 1: Scan for Single-Cell Regions
These are your easiest starting points. If a region has only one cell and target sum 5, that cell must be 5. Place any domino with a 5 there.
Step 2: Identify Large Equals Blocks
Regions with "=" constraints and multiple cells are very restrictive. If a 4-cell equals region has target 12, all cells must be 3 (since 3×4=12).
Check your domino inventory. If you only have one domino with a 6, and there's a cell that must be 6, that domino is committed.
Step 4: Work from Constraints
Look for cells with multiple constraints (e.g., "=" on one side and ">" on another). These "intersection" cells often have only one possible value.
Step 5: Use Elimination
If a cell can only be 0 or 6 (due to constraints), check which dominoes can provide those values. This often narrows down options quickly.
Step 6: Plan Ahead
Before placing a domino, consider how it affects remaining cells. Sometimes a "good" placement now creates problems later.
When stuck, try "what-if" analysis: if I place this domino here, what happens to the rest of the puzzle? This helps identify dead ends early.
❌ Common Mistakes to Avoid
Beginners often make these mistakes. Avoid them to solve puzzles faster:
1. Ignoring Domino Inventory
Don't forget to track which dominoes you've used. Running out of a specific value can make the puzzle unsolvable.
2. Placing Too Quickly
Take time to analyze constraints before placing. Hasty placements often lead to dead ends.
3. Forgetting About Holes
Remember that not all grid positions are active. Dominoes cannot extend into holes or outside the grid.
4. Overlooking Constraint Chains
Constraints can chain together: if A=B and B>C, then A>C. Look for these indirect relationships.
5. Not Using Undo
There's no shame in undoing moves! If you get stuck, backtrack and try different placements.
Every constraint must be satisfied simultaneously. A cell might satisfy its region sum but violate an "=" constraint with its neighbor. Both conditions must be true at once.
📊 Difficulty Levels Explained
NYT Pips offers three difficulty levels. Here's what to expect from each:
Easy (⭐)
- Smaller grids (typically 4×4 to 6×6)
- Fewer constraint types (mostly "=" and simple sums)
- Clear starting points with single-cell regions
- Good for learning the basics
- Average solve time: 5-10 minutes
Medium (⭐⭐)
- Larger grids (typically 6×6 to 8×8)
- More constraint types (adds "≠", ">", "<")
- Multiple interacting regions
- Requires planning ahead
- Average solve time: 10-20 minutes
Hard (⭐⭐⭐)
- Largest grids (can be 8×8 to 10×10)
- All constraint types in complex combinations
- Bottleneck cells that must be solved first
- Requires backtracking and advanced strategies
- Average solve time: 20-40 minutes
Start with Easy puzzles to build confidence. Once you can solve them consistently in under 10 minutes, move to Medium. Only attempt Hard puzzles after mastering Medium.