Question

The principal said they _ take part in the game

Answer 1

The principal said that they could take part in the game.

The sentence is in the simple past tense here indicated by the word 'said'. Therefore, you can use any of the past forms of the words can, will, shall, and may depending on what meaning and implication you would like the sentence to take.

1. The principal said that they couldn't take part in the game.
2. The principal said that they would take part in the game.
3. The principal said that they wouldn't take part in the game.
4. The principal said that they should take part in the game.
5. The principal said that they shouldn't take part in the game.
6. The principal said that they might take part in the game.
7. The principal said that they might not take part in the game.