25. Beatrix places dominoes on a $5 \times 5$ board, either horizontally or vertically, so that each domino covers two small squares. She stops when she cannot place another domino, as in the example shown in the diagram.
When Beatrix stops, what is the largest possible number of squares that may still be uncovered?
A 4
B 5
C 6
D 7
E 8
25. D First note that there are 25 squares on the board. As each domino occupies two squares, the number of squares left uncovered must be odd. The diagram on the right shows that it is possible for Beatrix to place the dominoes so that there are seven uncovered spaces when it is not possible for her to place any more dominoes.

Of the options given, it is not possible to obtain eight uncovered spaces as the number of them must be odd and it has been shown that seven uncovered spaces is possible so the correct answer is seven.
(For a proof that it is not possible to obtain more than seven uncovered spaces, please see the extended solutions on the UKMT website.)