TodayHint

Pips July 31, 2026: Hints & Answers

Constructed by Ian Livengood, Rodolfo Kurchan, Rodolfo Kurchan, edited by Ian Livengood.

Recap

The easy board requires logical placement of 5 dominoes in 6 regions. The medium board adds complexity with 7 dominoes and 9 regions. The hard board is the most challenging with 15 dominoes and 18 regions, requiring careful consideration of multiple constraints.

The three boards that day

The tray and each region's rule — board data, no solutions.

Easy board · 5 dominoes · 6 regions

4–25–22–23–54–4

  • two cells: exactly 7.
  • one cell: left uncovered.
  • one cell: under 3.
  • two cells: all matching.
  • one cell: more than 4.
  • three cells: all matching.

Small number of dominoes and regions makes it manageable.

Medium board · 7 dominoes · 9 regions

0–46–54–46–14–23–36–4

  • one cell: exactly 4.
  • one cell: under 4.
  • 3 ×two cells: exactly 6.
  • two cells: more than 6.
  • two cells: all matching.
  • one cell: left uncovered.
  • one cell: under 6.

More regions and dominoes add complexity.

Hard board · 15 dominoes · 18 regions

4–60–05–54–02–65–02–20–35–14–32–05–32–13–62–4

  • 2 ×two cells: exactly 10.
  • 3 ×one cell: exactly 3.
  • two cells: all matching.
  • two cells: under 3.
  • two cells: exactly 5.
  • one cell: exactly 2.
  • two cells: exactly 12.
  • 2 ×one cell: exactly 5.
  • three cells: exactly 0.
  • one cell: exactly 1.
  • two cells: exactly 6.
  • two cells: exactly 4.
  • two cells: exactly 3.
  • two cells: exactly 9.

Large number of dominoes and regions with complex constraints makes it challenging.

Pips hints, one rung at a time

Six rungs, easy board first. The recap above already named the walkthroughs, so this ladder is here for anyone replaying the boards fresh rather than as a spoiler shield.

  1. How the three boards compared

    Sizes and constraint mixes, counted off the boards.

    Easy board
    5 dominoes, 6 regions (2 equals, 1 empty, 1 greater, 1 less, 1 sum)
    Medium board
    7 dominoes, 9 regions (4 sum, 2 less, 1 empty, 1 equals, 1 greater)
    Hard board
    15 dominoes, 18 regions (16 sum, 1 equals, 1 less)
    Back to the board inventories
  2. Easy board: how to approach it

    Method only.

    Start by identifying regions with unique constraints, and look for dominoes that can only fit in one place.

  3. Easy board: where to start

    One region named by its constraint.

    The region with the 'greater 4' constraint over 1 cell is a good starting point.

  4. Medium board: approach and first region

    The same two steps, one difficulty up.

    Focus on regions with tight constraints like 'sum 4' and 'less 4', and try to place dominoes that satisfy multiple constraints.

    The region with the 'sum 4' constraint over 1 cell is a good starting point.

  5. Hard board: how to approach it

    Where the hard board differed in kind, not just size.

    Look for clusters of regions with interconnected constraints and try to place dominoes that satisfy multiple conditions.

  6. Hard board: where to start

    The last rung before the full walkthroughs.

    A region with a 'sum 3' constraint over 1 cell is a good starting point.

    Open the full walkthroughs

Every Pips walkthrough from that day

All three walkthroughs, folded: each one places every domino on its board, one after another.

  • Easy board · 5 dominoes

    Easy board walkthrough

    Place 4/2 in the 'sum 7' region, then 5/2 in the 'equals' region over 2 cells. Next, place 2/2 in the 'less 3' region. The 3/5 domino goes in the 'greater 4' region. Finally, place 4/4 in the remaining 'equals' region over 3 cells.

  • Medium board · 7 dominoes

    Medium board walkthrough

    Begin with the 'sum 4' region, then move to 'less 4' and 'equals' regions. Place 0/4 and 6/5 in the sum regions. The 4/4 domino fits in an equals region. Continue with the remaining dominoes, satisfying the constraints.

  • Hard board · 15 dominoes

    Hard board walkthrough

    Start by placing 0/0, 2/2, and 5/5 in sum regions. Then, place 4/6 and 2/6 in regions with high sum constraints. Continue with 5/0, 4/0, and 2/1 in less constrained areas. The 3/6 domino fits in a sum 9 region. Place 5/3, 2/4, and 4/3 in their respective sum and equals regions. Finally, place 5/1 and 0/3 in the remaining regions, ensuring all constraints are satisfied.

Those boards by the numbers

Date
Friday, July 31, 2026
Boards
3 — easy, medium, hard
Dominoes in play
27 across the three boards
Easy board
5 dominoes · 6 regions
Medium board
7 dominoes · 9 regions
Hard board
15 dominoes · 18 regions

More Pips

See the live Pips hints and answers page for the current boards, or browse every archived Pips date by month.

Try the other two puzzles