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UKMT Senior Kangaroo, 2024

Combinatorics Difficulty 2.0 Junior Prove it United Kingdom

At a football match between Glasgow Belles and Doncaster City, five supporters each made a prediction:

1. The game will end in a draw;
2. Glasgow will score;
3. Glasgow will win;
4. Glasgow will not lose;
5. Exactly five goals will be scored.

What is the maximum number of these predictions that could simultaneously come true?

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