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?

Word Ordering