## Coloured Squares

This puzzle also appears on tumblr, with a different description.

Imagine a card game where the rules are as follows:

You have a set of cards each with one of four colours - red, yellow, green, blue - and two players, named A and B.

Player B looks away while Player A deals out a 3x3 grid of cards at random.

Player A then takes more cards and deals out a second 3x3 grid so that each card in the original grid - the "bottom" grid - is covered by exactly one card in the new grid - the "top" grid. No card may cover a card of the same colour - a blue card can never be dealt on top of a blue card - so the "top" grid is not dealt out randomly.

Player B then points at a row or column and nominates one of the four colours. Player A then tells Player B how many cards of that colour are in that row or column.

Player B repeats this up to five times, for a total of six pieces of information.

Player B then guesses which coloured cards are in the bottom grid, card by card. Each correctly-guessed card is worth one point, with a one-point bonus if all nine are guessed correctly (for a maximum of ten points per round).

Suppose you are Player B, and Player A has given you this grid.

Suppose that you have been given the following pieces of information:

The far right-hand column has no red cards.

The middle row has two green cards.

The middle column has one green card.

The top row has two blue cards, and no yellow cards.

The bottom row has no blue cards.

As a free hint, Player A tells you that each colour is represented at least twice on the bottom grid.

What is the maximum number of points you can guarantee yourself?