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Students attending a masterclass at the Thomas Deacon Academy in Peterborough tried to work on this problem systematically. Here are examples of how they went about it.
I think their ideas are excellent and give an insight into how you might make a convincing argument that you have all possibilities. Well done to you all for trying to describe your approaches to this problem.
All the same E,E,E,E SE,SE,SE,SE I,I,I,I R,R,R,R - no 3 and 1 E,E,E,SE- no E,E,E,I - no E,E,E,R-no SE,SE,SE,E - no SE,SE,SE,I -no SE,SE,SE,R-no I,I,I,E - no I,I,I,SE I,I,I,R - no R,R,R,E R,R,R,SE - no R,R,R,I - no 2 and 2 ... ... ...
Even number of longs and shorts/does it work? | ||||
I | I | I | I | YES/YES |
EB | EB | EB | EB | YES/YES |
ES | ES | ES | ES | YES/YES |
R | R | R | R | YES/NO |
EB | EB | EB | I | NO |
EB | EB | EB | ES | NO |
EB | EB | EB | R | NO |
I | I | I | ES | YES/YES |
I | I | I | R | NO |
I | I | I | EB | NO |
R | R | R | I | NO |
R | R | R | ES | NO |
R | R | R | EB | YES/YES |
ES | ES | ES | I | YES/NO |
ES | ES | ES | EB | NO |
ES | ES | ES | R | NO |
EB | EB | I | I | YES/YES |
EB | EB | I | ES | YES/NO |