Great to see a Year 6 from a feeder school send us a brilliant and amusing solution to a question to a recent Olympiad paper. Good to know that there is hope for the youth!

Here is the question:

Here is the question:

**Her solution is below.**

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This problem is quite simple really. We have a row with a certain number of +s, and a certain number of -s. Let's call them pluses and minuses for now. A plus and a plus next to each other makes a plus, and a minus and a minus next to each other make a plus as well. However, a plus and a minus next to each other make a minus.

The key thing here is that there is one more minus than plus - that gives us the answer. Although this problem uses 2014 pluses and 2015 minuses, it doesn't matter the exact numbers - only that we have a number of pluses, and one more of minuses. Let's take 4 and 5 for example - 4 pluses, and 5 minuses.

[

**-**] [

**+**] [

**-**] [

**+**] [

**-**] [

**+**] [

**-**] [

**+**] [

**-**]

Let's call this the

**Start-off Phase**. We'll move on to the next phase,

**Phase One**. Let's convert the pairs of minuses and pluses into minuses.

**Start-off Phase:**[

**-**] [

**+**] [

**-**] [

**+**] [

**-**] [

**+**] [

**-**] [

**+**] [

**-**]

**Phase One:**[

**-**] [

**-**] [

**-**] [

**-**] [

**-**]

The little one on the end is still the same - it'll stay like that for a while, as an extra. That't the most important part of this problem, as you'll discover later. Now let's move on to

**Phase Two**.

**Start-off Phase:**[

**-**] [

**+**] [

**-**] [

**+**] [

**-**] [

**+**] [

**-**] [

**+**] [

**-**]

**Phase One:**[

**-**] [

**-**] [

**-**] [

**-**] [

**-**]

**Phase Two:**[

**+**] [

**+**] [

**-**]

As you can see, the two pairs of minuses have turned into pluses, as they should. The extra is still on the end, the odd one out.

**Start-off Phase:**[

**-**] [

**+**] [

**-**] [

**+**] [

**-**] [

**+**] [

**-**] [

**+**] [

**-**]

**Phase One:**[

**-**] [

**-**] [

**-**] [

**-**] [

**-**]

**Phase Two:**[

**+**] [

**+**] [

**-**]

**Phase Three:**[

**+**] [

**-**]

Still, the little fella is all alone. But it's about to get bigger in

**Phase Four**. Ooh, yes. Time for the final round.

**Start-off Phase:**[

**-**] [

**+**] [

**-**] [

**+**] [

**-**] [

**+**] [

**-**] [

**+**] [

**-**]

**Phase One:**[

**-**] [

**-**] [

**-**] [

**-**] [

**-**]

**Phase Two:**[

**+**] [

**+**] [

**-**]

**Phase Three:**[

**+**] [

**-**]

**Phase Four:**[

**-**]

There. As you can see, the fact there was an extra minus waiting in the shadows the whole time changed the whole thing - it leapt out and ate the the last plus left in

**Phase Four**. This problem is all about logic based on the mathematical file of odds and evens. Now I hope you fully understand the answer - the last symbol left is a

*minus*.