Thus replacing the ascending numbers with 8.5 in every cell and circling four cells gives a total of 34. Or as Natalie did, she realised that "you pick numbers from each column and row" and took the average between the sum of the four columns:
i.e. (28 + 32 + 36 + 40)/4 = 34
A good solution with this method came from Melanie and Rachel of Flegg High School.
A proof of this problem could be as follows.
Let the first number be a.
Then when choosing numbers from rows and column that do not
coincide we have:
4a + (4 + 8 + 12) + ( 1 + 2 + 3) = 34
i.e. 4a + 30 = 34
i.e a = 1
and the array is 1 through 16 as set.
But suppose the 'magic number' had been 62 then
4a + 30 = 62
i.e a = 8
and the array would have been 8 through 23.
Hope that the explanation above helps especially Josh at Russell Lower School to "work out where we went wrong".
We could have used a 5 by 5 array of ascending numbers!