Nine dots form a perfectly familiar figure. Four strokes seem almost sufficient, yet every natural route leaves something behind.
The Nine-Dot Puzzle
Riddle statement
Nine dots form a 3 × 3 grid.
Draw a single continuous path made of exactly four consecutive straight segments that passes through all nine dots, without lifting your pencil. You may start anywhere.
Show solution
Solution
Here is one valid path. Start at the bottom-left dot.
First segment: draw diagonally up and to the right, passing through the centre dot and ending at the top-right dot.
Second segment: draw straight down through all three dots in the right-hand column, then extend the line below the grid.
Third segment: from there, draw diagonally up and to the left; pass through the bottom-middle and middle-left dots, and continue until you are to the left of the top-left dot.
Fourth segment: turn right and draw a horizontal line through all three dots in the top row.
The four segments form one unbroken chain: each begins exactly where the previous one ends. The first covers the bottom-left, centre and top-right dots; the second completes the right-hand column; the third adds the bottom-middle and middle-left dots; and the fourth completes the top row. All nine dots are therefore covered without lifting the pencil.
The extensions beyond the grid are not decorative: they place two turns outside it and create the diagonal alignments the path needs. The difficulty comes from a restriction we tend to add unconsciously—the assumption that every segment must end on a dot or remain inside the square suggested by the layout. Neither condition appears in the puzzle.