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'Spotting the Loophole' printed from http://nrich.maths.org/

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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 closed loop.

Visually you can use lots of intuitive shortcuts, such as that 'long' arrows may need multiple 'short' arrows to close up into a loop.

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.