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Square Coordinates

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Spiral Snail

Stage: 3 Short Challenge Level: Challenge Level:1

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.
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