Question

No one of you can solve it -
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 different
squares 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?

Answer 1

Answer:

No one of you can solve it -

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 different

squares 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?