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

### Why do this problem?

This problem encourages students to use visualisation to help
them to spot a solution which can then be verified using algebra.
It shows students the power of using visual representations to
solve vector problems, often the quickest route to a
solution.

### Possible approach

This could form a short introduction to work on
vectors.

Display the example grids on the board, showing the three vectors
forming a closed loop and the four vectors on the right which do
not have a zero sum.

Then challenge students to find any closed loops in each of the
three grids.

When they think they have spotted a closed loop by eye, they should
verify algebraically that it is indeed a closed loop.

### Key questions

What can you say about the horizontal components of the
vectors in a closed loop?

And what about the vertical components?

### Possible extension

Vector
Walk begins to explore properties of vectors and combining two
basic vectors to reach points on the coordinate grid.

### Possible support

Students may find it helpful to draw the vectors on squared
paper.