Here is the full problem : Non-zero positive integers, not necessarily distinct, are written on the squares of an $8$ × $8$ chessboard (one number per square). At the beginning, five grasshoppers are on five differentsquares and hide the numbers. Gabriel calculates the sum of all the visible numbers and he obtains $100$. Simultaneously, each grasshopper jumps onto an adjacent square (it crosses a side shared by two squares). Gabriel calculates the sum of all the visible numbers and he gets $1000$. And so on, until he can no longer obtain a sum ten times greater than the previous one (when Gabriel calculates a sum, two grasshoppers are never on the same square). The total of the sixty-four numbers written on the chessboard is divisible by $35$ and it is the largest possible. What is this total?

This was the only problem on a math competition that I couldn't figure out and I still don't know how to solve it (I don't even know if I'm supposed to use number theory or combinatorics...) . The detailed solution isn't available on their website, the only thing that is said is that the answer is $11110785$. If anyone could help me figure out how to solve it, it would be appreciated!