# Last Piece of the Puzzle

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?)