One Stroke: Twin X
Read the puzzle
Four dot-and-line figures, A to D. A: a 2 by 2 grid of squares with both long diagonals crossing at the centre. B: six squares in a grid, three across and two down. C: two squares side by side, each crossed by both its diagonals. D: a 2 by 2 grid with both diagonals drawn only in the top-left and bottom-right squares, each X meeting at its own centre dot. Without lifting your pen and without going over any line twice, which figure can you draw?
Without lifting your pen and without going over any line twice, which figure can you draw?
Count the lines at each dot, including where the X lines cross.
D
Only D has 2 odd dots. The others have 4 or more.
How to solve it
Count the lines meeting at each dot, including the dots where X lines cross. A dot in the middle of the stroke is entered and left, so it needs an even number. Only the start and end can be odd, so the figure must have 0 or 2 odd dots.
A: each outer corner has two sides and a diagonal (3), and each side midpoint has 3. That is 8 odd dots.
B: the six dots along the outer edges, between the corners, each have 3 lines. Six odd dots.
C: the four outer corners each have 3 lines, and the two middle dots on the top and bottom each have 5 (two edges, the shared side and two diagonals). Six odd dots.
D: the top-left and bottom-right corners have 3 lines each. Every side midpoint has 4 (three grid lines plus one X arm), the centre has 6, the X centres have 4, and the other two corners have 2. Exactly 2 odd dots, so D works: start at the top-left corner and finish at the bottom-right.
The usual wrong pick is C, because its two crosses look symmetric and tidy. Its shared middle dots have 5 lines each, which makes too many odd dots.
Takeaway: diagonals can fix odd dots as well as create them, so always recount.
Learn the method: One-Stroke Drawing Puzzles: How to Solve Them by Counting Lines
