Quadrilaterals, tiling and the eight directions · Usually met around P4
Drawing in one stroke
Only 0 or 2 odd points can be drawn in one stroke.
How to do it
Method
Only 0 or 2 odd points can be drawn in one stroke
2 odd points: start at one of them
Another way
Try drawing it
Start at one odd point, end at the other
In full
Drawing in one stroke means never lifting the pen and never going over a line twice. First count the lines at each point: a point with an odd number is an odd point. With 0 odd points it can be done, and from any start you end where you began. With 2 it can be done too, but you must start at one odd point and finish at the other. With more than 2 it can't be done. In the famous seven bridges puzzle all four pieces of land have an odd number of bridges, so you can't cross every bridge exactly once. Or try drawing it, as a check.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
How many odd points (points with an odd number of lines) are in the drawing?
Show the answer and working
Answer: 4 points
Count the lines at each point: 4 have an odd number.
Example 2
To draw this in one stroke, which point should you start from?
- A. Point 1
- B. Point 3
- C. Point 5
- D. Point 2
Choose the right answer
Show the answer and working
Answer: B. Point 3
There are two odd points: start at one and finish at the other. Point 3 is odd.
Example 3
At least how many lines (each joining two points) must be added so the drawing can be done in one stroke?
Show the answer and working
Answer: 1 lines
There are 4 odd points; each line joining two of them removes 2, until 2 or fewer remain: 1.
Practise it in the game →Quadrilaterals, tiling and the eight directions · Free to start, unlimited questions, no download