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'Spiral Snail' printed from http://nrich.maths.org/
A sheet of graph paper is placed with its x
-axis pointing due East and its y
-axis pointing due North. A sluggish snail starts at point (0,0) and slowly, but smoothly, 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.
At which point does the snail finally arrive?
If you liked this problem, here is an NRICH task
which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.