7. Builders need to tile the floor in a small house with small square tiles. The client says that the variant with more red tiles is preferable. For variants with the same number of red tiles, the one with more orange tiles is preferable; and generally, the client's preferences for colors are: red, orange, yellow, green, blue, indigo. His wife, however, wants the opposite:

- the number of indigo tiles should be at least as many as the total number of red, orange, yellow, green, and blue tiles;
- the number of blue tiles should be at least as many as the total number of red, orange, yellow, and green tiles;
- the number of green tiles should be at least as many as the total number of red, orange, and yellow tiles;
- the number of yellow tiles should be at least as many as the total number of red and orange tiles;
- the number of orange tiles should be at least as many as the number of red tiles.

The floor requires 100 tiles.

How many green tiles will be needed if the most preferable variant for the client is chosen, which also meets the conditions set by his wife?
Answer: 13.

Solution: According to the conditions set by the customer's wife, there must be at least as many indigo tiles as all the others combined. This means there must be at least 50 tiles, which is half of all the tiles. The customer clearly wants the number of indigo tiles to be as few as possible. Therefore, in the desired variant, there will be exactly 50 indigo tiles.

Now we have moved to a similar problem: without the indigo color, and we need $100-50=50$ tiles. Reasoning similarly, we get that there should be 25 blue tiles.

And once again, we have moved to a similar problem: now without the blue color, and we need $50-25=25$ tiles. Then, in the desired variant, there will be 13 green tiles.

Comment: Continuing the reasoning, we will get the quantities of tiles of the other colors.