Question 7
Place the digits $1,2,3,4,5,6,7,8,9$ into each of the nine squares shown in the diagram below, using each digit exactly once.
The digit in each shaded square must be at least $3$ greater than the digit in every square sharing a side with it.
For example, if a shaded square contains the digit $9$, all squares sharing a side with it may contain any of the digits $1,2,3,4,5$ or $6$ but not $7$ or $8$.
In how many ways can the digits be placed in the diagram?
The digit in each shaded square must be at least $3$ greater than the digit in every square sharing a side with it.
For example, if a shaded square contains the digit $9$, all squares sharing a side with it may contain any of the digits $1,2,3,4,5$ or $6$ but not $7$ or $8$.
In how many ways can the digits be placed in the diagram?