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This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.)

 

On the table in front of you is a grid like this:-

 

 

Now imagine that you have another grid, just the same but made of plastic that you can see through.
You place the plastic one over the one on the table so that it covers it completely.
You could have flipped it over and/or turned it around as you put the plastic one down.
Then the numbers that are paired, one above the other, are multiplied together.
Finally, all the results of multiplying together will be added together.
 
Without doing the $36$ multiplications and then adding them together YOUR challenge is to say which way of flipping over and/or turning the plastic grid will give you the highest total and which way will give the lowest total.