Miss Braganza once decided to play a game with her students in class, who were beginning to look bored. She asked a peon to get an overhead projector (OHP) and focused a transparency sheet on a screen on the whiteboard. On the transparency sheet was a grid. There were 9 numbers in shaded squares on the grid in such a way that there were 8 non-shaded squares around each number. The game was that a student should fill each of the non-shaded squares with a number from 1 to 7.
The 8 numbers around the number in the shaded square should sum up to the shaded number.
Also, no row nor column should contain a duplicate number in the non-shaded square. For example, the top row may be 1 2 3 4 5 6 7.
Fill in the non-shaded squares with appropriate numbers and complete the grid.