Six dominoes have been placed in this grid and there is only one way of filing the grid with more dominoes. Try it:

We can do better than 6 dominoes. The way in which these five dominoes have been placed means that there’s only one way of completing the grid

Can we do better still?

These four dominoes lead to a unique tiling.

Better still! These three dominoes lead to a unique tiling.

What is the best you can do with other grids?

Number of columns

1 2 3 4 5 6 7 8

Number o rows

2 0 1 1 1 2 2 2 3

4 0 1

6 0 2 3

8 0 3

Valhalla

Val and Hal take it in turns to place a domino on the grid. Val places dominoes vertically and Hal places dominoes horizontally.

You can choose to be either Val or Hal. Your opponent then chooses whether to go first or second. The first player unable to place a domino loses.

Can you find a winning strategy?