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.
_____________________________________________________________________
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.
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