We start with a typical “fruit math” problem with 11 variables/fruits.

The fourth equation is a good place to start. After using the strawberry value to get a few other values (grape, watermelon, peach) easily, it becomes apparent that all the intended values are positive integers*, which makes the rest of the problem solvable quickly with guess-and-check.

Of note is that each of the 11 fruits appears uniquely as the right-hand side of one of the equations. Converting the values to letters via A=1, …, Z=26 and reading down yields a clue phrase:

*There is an alternate solution that uses non-integer values, but looking ahead to A1Z26 the values should deter solvers from pursuing this.

Image | Fruit | Value | Letter |
---|---|---|---|

grape | 19 | S | |

dekopon | 21 | U | |

peach | 9 | I | |

strawberry | 11 | K | |

pear | 1 | A | |

cherry | 6 | F | |

persimmon | 18 | R | |

apple | 21 | U | |

melon | 9 | I | |

watermelon | 20 | T | |

pineapple | 19 | S |

**SUIKA FRUITS** (matching the (5 6) enumeration at the bottom) is a reference to the mechanic of the recent viral hit *Suika Game*, where players combine fruits pairwise to make larger fruits in *2048*-like fashion. The 11 fruits in the game match the 11 fruits in this puzzle. (The English web version of the game refers to the persimmon as an orange, but the canonical fruit is a persimmon.)

Following the game’s mechanic, we combine the parenthesized pairs of fruits to get different fruits and a new system of 11 equations:

grape + strawberry - 14 = grape

strawberry + 9 = dekopon

31 - grape = peach

33 - grape = strawberry

37 - apple = pear

12 ÷ peach = cherry

watermelon = persimmon

252 ÷ strawberry = apple

strawberry + cherry - 9 = melon

dekopon - 18 = watermelon

This system of equations also resolves nicely to positive integer values, again aided by first identifying the strawberry’s value. The new values are:

Fruit | Value | Letter |
---|---|---|

cherry | 1 | A |

strawberry | 14 | N |

grape | 19 | S |

dekopon | 23 | W |

persimmon | 5 | E |

apple | 18 | R |

pear | 19 | S |

peach | 12 | L |

pineapple | 9 | I |

melon | 6 | F |

watermelon | 5 | E |

When read in the canonical ordering of the fruits in *Suika Game* from smallest to largest, the values-converted-to-letters match the (6'1 4) enumeration to spell ANSWER’S **LIFE**.