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Year 6 takes on the MOG with humour. Maths Olympiad for Giggles?

20/11/2015

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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:
Picture
Her solution is below.
_____________________________________________________________________
 
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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