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.

  1. (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, 47

    Ans: (a) ___

  2. (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

Sum=29+30+31+37+39+45+46+47=304\text{Sum} = 29 + 30 + 31 + 37 + 39 + 45 + 46 + 47 = 304

2. Calculate the average of the 8 numbers

Average=3048=38\text{Average} = \frac{304}{8} = 38

(Alternatively, by symmetry, the average of the 8 surrounding numbers is equal to the centre number, which is 3838.)

Answer

3838

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