MATE IN ONE BILLION MOVES

Dots represent number of pieces on a square. Think it as a kind of 3D chess.Think that pieces on a chess square stay top of each other.You can move them separately. 

White to move and mate in one billion.

Blue dot= 1000000000 chess pieces

Yellow dot =333333333 chess pieces

This problem cannot even be solved by super computers including Google Deepmind.

Solution is at depth 2 billion.

If you erase color dot representation, there is no mate for White. It is win for black.

For the correct solution both arithmetic and chess understanding is necessary.

Next time when someone asks you how many moves that you can calculate, tell them      at least one billion moves.

Lets say pieces can be top of  only its kind.But thanks, you understand the basic idea.

Rd8+ for 1 billion times. easier than ur mother