Pips July 22, 2026: Hints & Answers

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

Recap

The easy board requires logical placement of dominoes in regions with restrictive constraints. The medium board adds more complexity with various constraints. The hard board demands careful analysis of multiple constraints and domino placements.

The three boards that day

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

Easy board · 4 dominoes · 4 regions

Dominoes: 3–40–45–66–0

  • two cells: exactly 10.
  • two cells: exactly 4.
  • two cells: exactly 11.
  • two cells: under 4.

Small number of dominoes and regions makes this easy.

Medium board · 7 dominoes · 9 regions

Dominoes: 3–56–61–16–54–04–63–0

  • one cell: under 3.
  • 3 ×two cells: all matching.
  • 2 ×two cells: exactly 6.
  • 2 ×one cell: left uncovered.
  • one cell: more than 1.

More regions and dominoes increase the complexity.

Hard board · 16 dominoes · 18 regions

Dominoes: 2–63–02–10–52–43–50–23–35–42–34–16–60–43–15–53–4

  • 5 ×two cells: all matching.
  • one cell: exactly 5.
  • two cells: exactly 3.
  • three cells: all matching.
  • 2 ×one cell: exactly 1.
  • two cells: exactly 12.
  • 2 ×one cell: exactly 2.
  • three cells: exactly 0.
  • two cells: exactly 11.
  • three cells: exactly 13.
  • one cell: exactly 0.
  • one cell: more than 4.

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. Hint 1: How the three boards compared

    Sizes and constraint mixes, counted off the boards.

    Easy board
    4 dominoes, 4 regions (3 sum, 1 less)
    Medium board
    7 dominoes, 9 regions (3 equals, 2 empty, 2 sum, 1 greater, 1 less)
    Hard board
    16 dominoes, 18 regions (11 sum, 6 equals, 1 greater)
  2. Hint 2: Easy board: how to approach it

    Method only.

    Start by identifying regions with the most restrictive constraints and look for dominoes that can only fit in one place.

  3. Hint 3: Easy board: where to start

    One region named by its constraint.

    Begin with the region that must sum to 4 over 2 cells, as it has the smallest possible values.

  4. Hint 4: Medium board: approach and first region

    The same two steps, one difficulty up.

    Focus on regions with equality constraints and try to find dominoes that can satisfy multiple conditions at once.

    Start with an equals over 2 cells region, as it will help to fix the values of adjacent cells.

  5. Hint 5: Hard board: how to approach it

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

    Look for regions with the most restrictive constraints and try to find dominoes that can only fit in one place. Focus on sums and equals regions first.

  6. Hint 6: Hard board: where to start

    The last rung before the full walkthroughs.

    Begin with a sum 5 over 1 cell region, as it has a limited range of possible values.

Every Pips walkthrough from that day

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

  • Easy board · 4 dominoes

    Easy board walkthrough

    Place the 0/4 domino in the sum 4 region. Then, put the 5/6 domino in the sum 11 region. Next, place the 3/4 domino in the sum 10 region. Finally, put the 6/0 domino in the less 4 region.

  • Medium board · 7 dominoes

    Medium board walkthrough

    Begin by placing the 1/1 domino in an equals region. Then, put the 4/0 domino in an empty cell region. Continue with the 3/0 domino in a less 3 region. Place the 6/5 domino in a sum 6 region. Next, put the 4/6 domino in an equals region. Then, place the 3/5 domino in a sum 6 region. Finally, put the 6/6 domino in a greater 1 region.

  • Hard board · 16 dominoes

    Hard board walkthrough

    Start by placing the 2/3 domino in a sum 5 region. Then, put the 0/5 domino in a sum 5 region. Place the 3/0 domino in a sum 3 region. Continue with the 2/6 domino in a sum 8 region. Next, put the 5/4 domino in a sum 9 region. Then, place the 3/4 domino in a sum 7 region. Put the 5/5 domino in an equals region. Place the 6/6 domino in an equals region. Continue with the 3/1 domino in a sum 4 region. Next, put the 0/4 domino in a sum 4 region. Then, place the 2/1 domino in a sum 3 region. Put the 4/1 domino in a sum 5 region. Place the 3/5 domino in a sum 8 region. Next, put the 2/4 domino in a sum 6 region. Then, place the 0/2 domino in a sum 2 region. Finally, put the 3/3 domino in an equals region, and adjust the remaining dominoes accordingly to satisfy all constraints.

Those boards by the numbers

Date
Wednesday, July 22, 2026
Boards
3 — easy, medium, hard
Dominoes in play
27 across the three boards
Easy board
4 dominoes · 4 regions
Medium board
7 dominoes · 9 regions
Hard board
16 dominoes · 18 regions

More Pips

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