proofs 2

the 'Lo Shu'

this magic square consists of all the digits, from 1 to 9 inclusive

although there are a total of 8 rotations and reflections of it there is essentially one such magic square

what do 1 to 9 add up to?

what must each line total be?

think of some (good) reasons why the central number must be 5

by considering what numbers can be in the same line as 9, prove that 9 cannot occupy a corner position (and neither can 1)

by considering sums of odd and even numbers, prove that the corner numbers must all be even

given that 9 must be in a middle edge position, where must 8 go?