There are five or six puzzles that are variations of this, so I can't tell which you are referring to.
If it is the first one... the one with stone positions in a V-shape... the "sum of the grey tiles" is a red herring. The statement is true, but the actual answer needed on the stone is the sum of the surrounding red tiles.
Then there are some puzzles that follow that have stones based on the sum of the red tiles minus the sum of the blue tiles. Only include the tiles up to two positions from the center.
I never did figure out the basis for the last puzzle, so I just looked at the video. Last puzzle hint: The values of the Teddy Bear and the Guitar can be found in the stairwells in the NW and NE corners.