Question

00 piece jigsaw puzzle. the completed puzzle is 10x10. each piech connects to at least 2 other pieces. i plan to assemble by taking pieces out of box one by one. if i've already taken out 2 pieces that dont directly connect, what is the minimum number of additional pieces that i need to draw to in order to guarentee that the original 2 pieces connect?

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Neal

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71 Answers

In a 10x10 jigsaw puzzle, each piece connects to at most 4 other pieces - top, bottom, left, and right.
The corner pieces connect to 2 other pieces, the edge pieces connect to 3, and the rest connect to 4.
If you have 2 pieces that don’t directly connect, the minimum number of additional pieces you need to guarantee a connection depends on their relative positions:
If the two pieces are corner pieces from the same edge (top, bottom, left, or right), you need 1 additional piece to connect them.
If the two pieces are corner pieces from different edges, you need 2 additional pieces to connect them.
If one piece is a corner piece and the other is an edge piece on the same edge, you need 1 additional piece to connect them.
If one piece is a corner piece and the other is an edge piece on a different edge, you need 2 additional pieces to connect them.
If both pieces are edge pieces on the same edge, you need 1 additional piece to connect them.
If both pieces are edge pieces on different edges, you need 2 additional pieces to connect them.
If one or both pieces are inside pieces (not on an edge), you need 2 additional pieces to connect them.
So, in the worst-case scenario, you need to draw 2 additional pieces to guarantee that the original 2 pieces connect. This would be the case if the two pieces are on different edges or if one or both are inside pieces. In all other cases, you would only need to draw 1 additional piece.

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