One Stroke: Strip
Read the puzzle
Four dot-and-line figures, A to D. A: two squares side by side, the left one crossed by both diagonals meeting at a centre dot. B: a row of three squares. C: a 2 by 2 grid of squares with both diagonals drawn only in the top-left square. D: a 2 by 2 grid with one diagonal from the top-left corner to the centre, and both diagonals in the bottom-right square. 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. More than 2 odd dots means no.
A
A has only 2 odd dots. B, C and D each have 4.
How to solve it
Count the lines that meet at each dot. Every time the pen passes through a dot it uses one line in and one line out, so in-between dots need an even count. Only the start and the end may be odd. A figure with more than 2 odd dots cannot be drawn in one stroke.
A: the two left corners have a side, an edge and a diagonal, 3 lines each. The two middle dots have 4 (two edges, the shared side and a diagonal). The right corners have 2 and the X centre has 4. Just 2 odd dots, so A can be drawn, starting at one left corner and ending at the other.
B: the four middle dots of the strip each have 3 lines, so 4 odd dots.
C: the top-left corner (3), the centre (5), the middle of the right side (3) and the middle of the bottom (3) are odd. Four odd dots.
D: the top-left corner (3), bottom-right corner (3), the middle of the top (3) and the middle of the left side (3) are odd. Four odd dots.
The usual wrong pick is B, the plain strip, because it has no diagonals. But its four T-shaped junctions are all odd. Takeaway: count odd dots, not lines.
Learn the method: One-Stroke Drawing Puzzles: How to Solve Them by Counting Lines
