Spiral Snail
A snail slithers around on a coordinate grid. At what position does he finish?
Age
11 to 14
Challenge level
Problem
A coordinate grid has its x-axis pointing due East and its y-axis pointing due North.
A sluggish snail starts at point (0,0) and slowly slithers 1 unit North, 2 units East, 3 units South, 4 units West, 5 units North, 6 units East, 7 units South, 8 units West, 9 units North and (lastly!) 10 units East.
What are the coordinates of the snail's finishing point?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $(6,5)$
Tracing the journey
Image
Adding the moves
The distance it moves East $=2-4+6-8+10=6$.
The distance it moves North $=1-3+5-7+9=5$.