TodayHint

Pips July 30, 2026: Hints & Answers

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

Recap

The easy board requires strategic placement of 5 dominoes to meet sum and equality constraints. The medium board adds more dominoes and varied constraints, requiring careful planning. The hard board features 16 dominoes and complex constraints, demanding a systematic approach to solve.

The three boards that day

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

Easy board · 5 dominoes · 7 regions

5–51–65–65–14–1

  • 2 ×one cell: exactly 5.
  • one cell: left uncovered.
  • 2 ×two cells: all matching.
  • one cell: under 4.
  • two cells: exactly 10.

Small number of dominoes and simple constraints make this easy.

Medium board · 7 dominoes · 7 regions

1–46–34–52–30–54–65–3

  • two cells: exactly 5.
  • 2 ×three cells: exactly 15.
  • 2 ×one cell: left uncovered.
  • three cells: all matching.
  • one cell: more than 2.

More dominoes and varied constraints increase the challenge.

Hard board · 16 dominoes · 24 regions

0–10–20–30–40–51–21–31–41–52–32–42–53–43–54–53–6

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

Large number of dominoes and complex constraints make this 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, 7 regions (3 sum, 2 equals, 1 empty, 1 less)
    Medium board
    7 dominoes, 7 regions (3 sum, 2 empty, 1 equals, 1 greater)
    Hard board
    16 dominoes, 24 regions (21 sum, 3 equals)
    Back to the board inventories
  2. Easy board: how to approach it

    Method only.

    Start by identifying regions with the fewest possible domino combinations.

  3. Easy board: where to start

    One region named by its constraint.

    Begin with the region that must sum to 5 over a single cell.

  4. Medium board: approach and first region

    The same two steps, one difficulty up.

    Look for regions with fixed sums or differences to place dominoes.

    Start with a region that has an empty constraint.

  5. Hard board: how to approach it

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

    Focus on regions with small sum constraints to start placing dominoes.

  6. Hard board: where to start

    The last rung before the full walkthroughs.

    Begin with a region that must sum to 1 over a single cell.

    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 the 5/5 domino, then use the equals constraints to place the 5/6 and 5/1 dominoes. Next, place the 4/1 domino to satisfy the sum 5 and less 4 constraints. The remaining dominoes will fit into the empty regions.

  • Medium board · 7 dominoes

    Medium board walkthrough

    Begin by placing dominoes that satisfy the sum 15 over 3 cells, then use the equals constraints to place other dominoes. The empty regions will help guide the placement of the remaining dominoes.

  • Hard board · 16 dominoes

    Hard board walkthrough

    Start by placing the 0/1 domino to satisfy the sum 1 constraint. Then, place dominoes that meet the sum 3 and sum 4 constraints. Use the equals constraints to place dominoes in regions with multiple cells. Continue this process, using the constraints to guide the placement of dominoes. The sum 10 over 2 cells constraint will help place higher-value dominoes. As the board fills, use the remaining constraints to ensure all dominoes fit.

Those boards by the numbers

Date
Thursday, July 30, 2026
Boards
3 — easy, medium, hard
Dominoes in play
28 across the three boards
Easy board
5 dominoes · 7 regions
Medium board
7 dominoes · 7 regions
Hard board
16 dominoes · 24 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