In the game of MIM, each of two players, Alice and Bob, receive a board as shown below:
They are then dealt in turns one card from a shuffled set of cards numbered 0 through 9 which they must immediately place in one of the empty boxes of their board (and not move again). Once all cards have been dealt and placed, products of the two resulting multiplications are found. The winner is whoever gets the larger result.
After four cards had been dealt and placed as shown below (Alice's board on the left), Alice is dealt card numbered 7. Where should she place this card for her best chances to win the game?
What if the object of the game is to obtain the smallest of the two products?