The solution to the nine dots puzzle requires thinking 'outside the box' by extending the lines beyond the perceived square boundary formed by the dots. The four continuous straight lines are drawn in sequence: 1) Horizontally across the top row of dots, extending past the final dot. 2) Diagonally down and to the left, passing through the middle-right and bottom-middle dots, and extending beyond the boundary. 3) Vertically up through the three dots in the left-most column. 4) Diagonally down and to the right, passing through the center dot and ending on the bottom-right dot, completing the connection of all nine dots.