FIVE people make the following statements:-

(1) | Either | (a) 3's statement is false and 4's statement is true. |

Or | (b) 2's and 5's are both false. | |

(2) | Either | (a) 4's statement is false or 3's is false. |

Or | (b) 1's and 5's are both false. | |

(3) | 2's statement is true or 4's and 5's are both true. | |

Moreover, either 5's is false or 4's is true. | ||

(4) 3's statement is false or 1's is true. | ||

(5) Fermat's last theorem is true. |

Which of these statements are true and which false? It will be found on trial that there is only one possibility. Thus, prove or disprove Fermat's last theorem.

*Eureka*,
**9**.

Reproduced from Eureka 27 page 35.

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