Winning Move

Free puzzles to print

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

• Level 1

  Ages 4–6 · Pre-K–K

  

  Finish the line (stars and moons on a 3 × 3 board): first, check the one square that makes three stars in a row. Then the same with decoys, such as the moons' pairs, or star pairs that are already blocked. The hardest: you can't win, so draw a star in the one square that stops the moons' line.

  On the sheet: “Finish the line: three stars in a row.”

  Print Level 1 (Letter)Other paper size: A4

• Level 2

  Ages 6–8 · Grades 1–2

  

  Tic-tac-toe (you are X): first win now, then block the square that stops O from winning. The hardest: make two threats at once so you must win.

  On the sheet: “Tic-tac-toe: find the move.”

  Print Level 2 (Letter)Other paper size: A4

• Level 3

  Ages 8–10 · Grades 3–4

  

  Nim: first two piles (make them equal), then bigger piles or the "take 1, 2 or 3" game. Next, three small piles, using a short list of safe positions; the hardest have three piles of up to 7.

  On the sheet: “Nim: find the move that wins.”

  Print Level 3 (Letter)Other paper size: A4

• Level 4

  Ages 10–12 · Grades 5–6

  

  Dots and boxes, on a 2 × 2 box board: first count how many boxes you can take now. Then find the one line that gives nothing away. The hardest, on a 2 × 3 box board, are endgames where every line gives something away and one is best.

  On the sheet: “Dots and boxes: find the move.”

  Print Level 4 (Letter)Other paper size: A4

The thinking it works on

• Taking the other player's view

  Asks what the opponent will do after each move.

  In Sher, Koenig and Rustichini's (2014) games, 3- to 9-year-olds grew more strategic with age on their very first move. From about age 7 they began to think about the other player's choices in a farsighted rather than a short-term way. Source

• Looking ahead

  Pictures the game one or two turns from now.

  Raijmakers and colleagues (2014) found that strategy use in a turn-taking game was linked to age from 5 to 12. No child yet used the best two-step strategy. Source

• Spotting three in a row

  Scans every line for two alike and an empty third.

• Ordering goals

  Win first, block second, then plan.

  Crowley and Siegler (1993) found that young children's tic-tac-toe play is built from rules picked up one at a time. Even young children shift which rule they apply as the position changes. Source

• Finding a pattern that always works

  Uses positions that are safe to leave.

• Weighing gains and losses

  Picks the move that gives away the least.

  Crone and van der Molen (2004) compared 6- to 9-year-olds, 10- to 12-year-olds, teenagers and adults on a choice task. Sensitivity to the later results of a choice, good or bad, increased with age. Source

Where is this thinking used?

• Family game night: Seeing a threat coming and blocking it in time.
• Sharing and turn-taking: Thinking about what the other person will want next.
• Saving and spending: Giving up a little now to avoid losing more later.
• Sports tactics: Setting up two chances at once so a defender can stop only one.