# Truth Table

## Answer: CHERRY TOMATO

## By Ben Coukos-Wiley

To solve the puzzle, find both solutions to the logic puzzle. The best place to start is the self contained logic loop of Green-2, Green-3, White-1, Scarlett-1, and Mustard-3. But this isn't the only way to go: assigning an arbitrary statement as true or false and following the line of implication will usually lead to either a solution or a contradiction. At the end of each solution you should have determined the truthfulness of all statements and assigned every person a fruit. We then convert each person's four statements into a number by interpereting it as four-digit binary, then we use that number to index their fruit. Reading around the table in the order statements are given in gets us:

### Solution 1

Person | Fruit | S1 | S2 | S3 | S4 | Index | Letter |
---|---|---|---|---|---|---|---|

Mr. Green | FREESTONE PEACHES | T | T | F | T | 13 | C |

Miss Scarlett | CHAMPAGNE GRAPES | F | F | T | F | 2 | H |

Colonel Mustard | EUROPEAN CANTALOUPE | F | F | F | T | 1 | E |

Professor Plum | ASIAN PEAR | T | F | F | T | 9 | R |

Mrs. Peacock | BLOOD ORANGE | F | T | T | T | 7 | R |

Mrs. White | DANCY TANGERINE | F | T | F | T | 5 | Y |

### Solution 2

Person | Fruit | S1 | S2 | S3 | S4 | Index | Letter |
---|---|---|---|---|---|---|---|

Mr. Green | EUROPEAN CANTALOUPE | T | T | F | F | 12 | T |

Miss Scarlett | FREESTONE PEACHES | F | T | T | T | 7 | O |

Colonel Mustard | CHAMPAGNE GRAPES | F | T | F | F | 4 | M |

Professor Plum | ASIAN PEAR | F | F | F | T | 1 | A |

Mrs. Peacock | DANCY TANGERINE | F | T | T | F | 6 | T |

Mrs. White | BLOOD ORANGE | F | T | F | F | 4 | O |

Each gives half the answer, and putting them together gets CHERRY TOMATO - a fruit you wouldn't want to find in your bowl of fruit salad.