Each cell of a $10 \times 10$ table is filled with a non-negative integer , two numbers in this table are called adjacent whenever the cells containing these two Have a common side . We are looking for a table which has these two following features:
A) difference of every two adjacent number should be $0$ or $1$ .
B) if a number is less than or equal to all adjacent numbers, In this case, it must be $0$.
How many of these tables can we made?
Using the first condition (A) I proved there should be a integer which repeat at least $10$ times in the table , but I wasn't successful to apply second condition in a way that leads me to the solution.
Any help is appreciated , thanks!