One Stroke: House
Read the puzzle
Four dot-and-line figures, A to D. A: a square with both diagonals crossing at a centre dot. B: the same crossed square with a triangular roof on top, its peak dot joined to both top corners. C: six squares in a grid, three across and two down (4 by 3 dots). D: a row of three squares (4 by 2 dots). 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.
B
Only B has just 2 dots where an odd number of lines meet: start at one, end at the other.
How to solve it
Count the lines meeting at every dot and mark each dot odd or even. A one-stroke drawing passes through a dot by going in and out, which uses lines in pairs. Only the start and end dots can have an odd number, so a figure can be drawn in one go only if it has 0 or 2 odd dots.
A: each corner of the crossed square has two sides and a diagonal, 3 lines. That is 4 odd dots, so no.
B: the roof peak has 2 lines. The top corners each have a roof line, the top edge, a side and a diagonal, 4 lines. The centre has 4. Only the two bottom corners have 3 lines. Exactly 2 odd dots, so B works: start at one bottom corner and finish at the other.
C: the six dots on the outer edges between corners each have 3 lines. Six odd dots, so no.
D: the four middle dots on the top and bottom each have 3 lines. Four odd dots, so no.
The usual wrong pick is A, because it looks simpler than the house. Adding the roof is what fixes it: the roof gives each top corner one extra line and turns two odd dots even.
Takeaway: more than 2 odd dots means it cannot be done.
Learn the method: One-Stroke Drawing Puzzles: How to Solve Them by Counting Lines
