The table below shows numbers from 1 to 56. Kai and Ray are given a plastic frame that covers exactly 9 squares of the table with the centre square covered.

- (a)
Kai puts the frame on the 9 squares shown in the figure below. What is the average of the 8 numbers that is seen in the frame below?
(The 3-by-3 area shown has the following numbers)
Top row: 29, 30, 31
Middle row: 37, (centre covered), 39
Bottom row: 45, 46, 47Ans: (a) ___
- (b)
Ray puts the frame on another 9 squares.
The sum of the 8 numbers that can be seen in that frame is 344.
What is the sum of all the even numbers that Ray can see in that frame?Ans: (b) ___
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Worked solution
15(a)
1. Calculate the sum of the 8 visible numbers
2. Calculate the average of the 8 numbers
(Alternatively, by symmetry, the average of the 8 surrounding numbers is equal to the centre number, which is .)
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