In the grid shown, we need to fill in the squares with numbers so that the number in every square, except for the corner ones, is the average of its neighbours. The edge squares have three neighbours, the others four.
What is the value of the number in the square marked x?
My way is too hard: I set pronumerals a,b,c,d,e,f,g,h, and find all other cells expressions about x,a,b,c,d,e,f,g,h. for example, the top row, second column is (a+x+1000)/3, etc. Then I have Multivariate linear equations. It is too hard to solve it.
Any one has a better method?