One Stroke: Tall
Read the puzzle
Four dot-and-line figures, A to D. A: a 2 by 2 grid of squares with one diagonal from the top-left corner through the centre to the bottom-right corner. B: a row of three squares, the left one with a diagonal from top-left to bottom-right. C: two squares stacked, the top one with a diagonal from top-left to bottom-right. D: a 2 by 2 grid plus a diamond joining the four outer side midpoints. 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. Odd dots must be the start or the end.
C
C has only 2 odd dots. A has 6; B and D have 4.
How to solve it
For each figure, count how many lines meet at every dot. A dot the pen passes through uses lines in pairs, so it must be even. Only the start and end of the stroke can be odd, which means the figure needs 0 or 2 odd dots.
A: the top-left and bottom-right corners each have 3 lines (two sides and the diagonal), and all four side midpoints have 3. That is 6 odd dots.
B: the top-left corner (3), the second top dot (3), the third top dot (3) and the third bottom dot (3) are odd. The second bottom dot has 4 because the diagonal ends there. Four odd dots.
C: the top-left corner has 3 lines and the middle-left dot has 3. The middle-right dot has 4, since the diagonal lands there, and the other corners have 2. Exactly 2 odd dots, so C can be drawn: start at the top-left corner and end at the middle-left dot, or the reverse.
D: each of the four side midpoints has 5 lines, so 4 odd dots.
The usual wrong pick is D, because its pattern looks balanced. Balance does not matter; parity does.
Takeaway: exactly 2 odd dots means yes, and they tell you where to start and finish.
Learn the method: One-Stroke Drawing Puzzles: How to Solve Them by Counting Lines
