Nine people are sitting in the squares of a 3 by 3 grid, one in each square, as shown. Two people are called neighbours if they are sitting in squares that share a side. (People in diagonally adjacent squares, which only have a point in common, are not called neighbours.)
Each of the nine people in the grid is either a truth-teller who always tells the truth, or a liar who always lies.
Every person in the grid says: ‘My neighbours are all liars’.
Given only this information, what are the smallest number and the largest number of people who could be telling the truth?
| smallest | largest | |
|---|---|---|
| A | 1 | 4 |
| B | 2 | 4 |
| C | 2 | 5 |
| D | 3 | 4 |
| E | 3 | 5 |
| F | 4 | 4 |
| G | 4 | 5 |
| H | 5 | 5 |
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