The magic square
1 9 5 6 2 7 8 4 3 The first square is attached above. Surprisingly it did not take too long and I did not write it down as a formal problem. Rather, I simply noted that the numbers 1+2+3+...+9 = 45 exactly. The connection is that we are told (actually we don't need to be told) that each column and row has to sum to 15. This is 45/3, so that seems to be useful. I started by putting 1 in the upper left corner, and hence I need bigger numbers on the row to make 15. I chose 9 and then 5. Now working down at the first column from the left, since I have used 9 I want something big so I pick something like 8. This seems to work fine and I was able to complete them row and column wise. The problem arises when considering the diagonals, they are way off at 1 + 2 + 3. To try it more, I start by considering the diagonals, and complete an X in th...