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'Spotting the Loophole' printed from http://nrich.maths.org/
In order to solve this problem you will need to think about what
makes a loop closed instead of open.
In two dimensions the overall changes in the x direction around the
loop must cancel out and the overall changes in the y directions
around the loop must also cancel out. You can think about these two
directions separately if you cannot quickly spot how to form a
Visually you can use lots of intuitive shortcuts, such as that
'long' arrows may need multiple 'short' arrows to close up into a
Of course, when you think that you have spotted a loop you will
need to check carefully to see
if you are correct by adding up the vectors exactly.