GeekDad Puzzle of the Week: The Invasion - Solution!

Summer is upon us, and here in Central Florida we have something besides hurricanes to worry about. We have to contend with a horrible enemy that is difficult to kill and persistent in it’s mission. The enemy? Red Ants. Impervious to most household poisons and determined in their mission to dominate every empty lot between Key West & Pensacola. There is an empty lot in my neighborhood, and the Red Ants are working on their domination of the crab grass and miscellaneous weeds. I need your help to figure out how long before the Red Ants take over the lot and pose a threat to the neighbors.

And help I did receive! While the best suggestion was just to lay down a heavy layer of Amdro, I was actually looking for an estimate of how many days until the ants took over. And the winner is Rick Greenlee who correctly figured 12 Days. He just won a $50 gift code from Thinkgeek!

The original puzzle is as follows:

Here’s what I know about the ants, based on carefully measuring the lot and making up facts about their reproductive cycle. I have also noticed some black ants on the lot, and I put down some poison just to see what would happen.

The lot is 25 squares, each square measuring three square feet.

In 12 squares, Black ants occupy one square foot of each of those squares. The Black ants do not reproduce.

It takes 10 Red Ant soldiers to defeat the black ants on a square. I noticed those Red Ants died after battle.

The Red Ant queens reproduce five soldiers per day and one queen every other day.

It takes seven Red Ant soldiers to occupy one square foot and one queen per three square feet to occupy a space and own it.

I put poison down in eight empty spaces, covering all three square feet of each space. The poison does not kill the queens, but it kills three soldiers per space per day.

The Red Ants currently occupy one space containing one queen and 20 soldiers and no Black ants or poison. Based on that, how many days until they fully occupy the remaining 24 spaces and have taken over the lot?

In all strategic military conflicts, first you amass your army – then you attack your enemy. In this case the enemy being the Black Ants, the poison and the yard in general.

The Red Ants will be ready for occupation on Day 12, at which time they will send their armies forth!

120 Will die fighting the black ants.

40 will die on the poison spaces.

There will be 805 soldiers left to populate the spaces, where only 525 are needed (this is assuming that the puzzle and the poison ends here, otherwise the answer is infinite.)

Only 25 Queens are needed, and they were ready by Day 10.

Day Queens Soldiers Dead (Black Ants) Dead (Poison)

1 1 25 | |

2 2 35 | |

3 2 45 | |

4 4 65 | |

5 4 85 | |

6 8 125 | |

7 8 165 | |

8 16 245 | |

9 16 325 | |

10 32 485 | |

11 32 645 | |

12 64 965 120 40

13 64 1285 | |

14 128 1925 | |

15 128 2565 | |

16 256 3845 | |

17 256 5125 | |

18 512 7685 | |

19 512 10245 | |

20 1024 15365 | |

<p>Thanks to all who submitted answers! Your 10% off code for <a href="http://thinkg.com/" target="blank">Thinkgeek!</a> is Puzzling! Tune in M to win!</