Two-Trait Grid

Free puzzles to print

Each set: a Learn sheet with a worked example, 10 puzzles from easiest to hardest, and the answers.

• Level 2

  Ages 6–8 · Grades 1–2

  

  A 3 × 3 grid with five or six whole clues, then three or four. The hardest puzzles give half clues: a shape with a "?" (find its fill) or a paint drop with a "?" (find its shape).

  On the sheet: “Each row and column has each shape once and each fill once. No pair twice. Draw the missing ones.”

  Print Level 2 (Letter)Other paper size: A4

• Level 3

  Ages 8–10 · Grades 3–4

  

  A 4 × 4 grid with six or seven clues, then four or five. Next come six clue cells, half of them half clues; the hardest puzzles have only five clue cells.

  On the sheet: “Each row and column has each shape once and each fill once. No pair twice. Draw the missing ones.”

  Print Level 3 (Letter)Other paper size: A4

• Level 4

  Ages 10–12 · Grades 5–6

  

  Easier puzzles: seven or eight whole clues, then five or six.

  Harder puzzles: six clue cells where every second one is a half clue, plus corner-mark size clues. The hardest puzzles have five clue cells and need a chain of "that pair is already used" steps.

  On the sheet: “Each row and column has every shape once, every fill once, and 2 big and 2 small. No shape and fill pair is used twice. Draw the missing ones.”

  Print Level 4 (Letter)Other paper size: A4

  The sheet is titled “Three-Trait Grid”.

The thinking it works on

• Holding two features in mind

  Thinks about shape and fill for every cell.

  Alloway, Gathercole and Pickering (2006) found that in children aged 4 to 11, the same parts of working memory were in place from age 4 and stayed stable. They included a separate store for what things look like and where they are. Source

• Reasoning by elimination

  Finds what is missing from a row or column.

  Birney, Halford and Andrews (2006) built a one-rule shape-grid puzzle and tested 204 students aged 8 to 19. Items that needed more of the grid weighed together were harder. Source

• Using every pair once

  Keeps track of which shape-and-fill pairs are used.

  English (1993) asked 7- to 12-year-olds to dress toy bears in every mix of tops and pants; strategies ran from trial and error to holding one item fixed. Source

• Keeping a record

  Lists used pairs so memory is free for the next step.

  Bulley and colleagues (2020) offered children aged 4 to 11 a way to mark hidden locations. The children took it up quickly, and used it more when the memory task was harder. Source

• Reasoning from half clues

  Uses a clue that gives only the shape or only the fill.

• Juggling three rules

  Keeps shape, fill and size rules apart and together.

  Huizinga, Dolan and van der Molen (2006) tested 7-, 11-, 15- and 21-year-olds. Holding and working with information in mind kept developing into young adulthood, and switching between rules into adolescence. Source

Where is this thinking used?

• Experiments: Scientists arrange tests so every pairing of two factors shows up once.
• Sports schedules: Each team plays on each field and at each time once.
• Seating plans: No table gets two people from the same group.
• Gardens: Each bed gets each crop once over the seasons.