This is called a zero-knowledge proof. Since you only show a part of the map's coloring to your opponent, they don't know the exact coloring method (answer).

But by the time he and his four collaborators published this “packing coloring” problem in the journal Ars Combinatoria in 2008, they had proved that it can be solved using 22 numbers.

5.Tape the sheets together to form a single 36 x 24 inch map, but don't tape on the front where you will be coloring. 6.Color the regions and flags with sharp pencils.