Jigsaw puzzles can be easy or hard, and it all depends on three things. First, there are the shapes: If they all look the same, that’s harder than shapes that don’t match. Then there’s the number of pieces you have to put together: If your puzzle has just 2 rows with 3 pieces in each, that’s a lot fewer steps than a crazy 1,000-piece puzzle. But most important of all is the size of the pieces compared to the size of the picture you’re making. If a red apple uses just 4 pieces, that’s much easier than if that apple covers 40 pieces or 400; they’ll all look the same. All that said, we’re pretty sure that the world’s biggest jigsaw puzzle takes a lot of work. It has more than 40,000 pieces, and stretches 22 feet long! If there’s an apple anywhere on there, let’s hope it doesn’t use a whole 5,000 pieces by itself.
Wee ones: If you add a blue piece to your puzzle, then a red, then a green, then a blue again to start over, then a red again…what piece do you add next?
Little kids: If your puzzle has 3 rows with 3 pieces in each, how many puzzle pieces does it have in total? Bonus: If the vacuum sucks up 3 of those pieces, your dog licks up 2 pieces, and 2 pieces get mixed in with some other puzzle, do you have any pieces left?
Big kids: A lot of people like to make the border (edge) of the puzzle first, then fill in the center. If a puzzle has 6 rows of 4 pieces, each, how many of those pieces are edges or corners? (Hint if needed: There are 2 long sides and 2 short sides, but don’t double-count the corners!) Bonus: Now if you have a 7-piece-wide by 7-piece-tall puzzle, how many pieces are NOT on the edges? (Hint if needed: Can you find a shortcut without adding and subtracting?)
Answers:
Wee ones: A green piece, since the pattern is blue-red-green.
Little kids: 9 puzzle pieces. Bonus: Yes! You still have 2 pieces.
Big kids: 16 edge pieces: 6 along each long edge (12 total) plus 2 more non-corners on each short edge (4 more). Bonus: 25 pieces. If you take away all the edges, you’re left with a 5 x 5-piece square in the middle!
Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.