Life is A Test 2: Test Harder (Quite A Bit Harder)

by Brony_of_Brody

And Then We Entered A Completely Different Genre Altogether

Upon hitting the Enter key on the innocuous device, the trap suddenly springs to life, and from the little package, it suddenly transforms into what appears to be a giant mechanical crab about twenty-four feet high. Before you can argue that such a feat should be impossible for a small cube about six inches wide, it emits a high-pitched whine, and from who knows where, the Apple-Crab emerges from its hiding place and begins to square down the crab.

You recall from the instruction manual that upon sighting its target, the package will execute what the manual referred to as "Protocol B-10-Up", which causes the device to enter a combative stance, warning that it would become "a swirling vortex of metal, fleshy remains of your target pest, and violence", and could create "profoundly disturbing scenes".

Unfortunately, nopony could ever have known that Apple-Crabs have a spontaneous biological process inside their bodies that automatically trigger when encountering a threat larger than itself: it can expand its body to match the size of the threat, and very soon you have two twenty-four foot tall crabs brawling in the middle of Sweet Apple Acres.

The farm is quickly evacuated, to Big Macintosh, Applebloom and Granny Smith's confusion, with only you and Applejack choosing to remain to monitor the situation. The brawl is long and intense, but suddenly, the Apple-Crab grabs your mecha in a vice, and to the shock of everypony watching, the mecha directly assimilates the Apple-Crab directly into its own body.

This however proves to a costly mistake and soon the crab's consciousness begins to override that of the mecha, and recognising a target, it begins to devour the apples in the trees at a rapid pace, its new mechanical body protecting it from the heat of the day. The only way now to contain the threat once and for all is to destroy the mecha-Crab entity down to its very foundations.

From what you could remember from the instruction manual, the device has one-hundred exhaust ports, and you propose that blocking up some of them would cause the mecha-Crab to cease to function and destroy itself. Suddenly, the crab turns on the pair of you, but in a display of strength and sheer unadulterated stones (if a mare like Applejack had any), she leaps onto the bio-mechanical foe and tells you to look up where the exhaust ports can be found.

After a few minutes (and several bruises inflicted on the orange mare), you read that the exhaust ports are located at the base of the legs. Rather less fortunately, the mecha will automatically close such ports upon sustaining damage, but that further damage would then cause every second port to remain open, while the other half closed off, then every strike would cause every third exhaust port to toggle open or closed, depending on position.

You recall that in the fight between the Apple-Crab and what is rapidly turning out to be a waste of bits, the mecha was struck a total of exactly one hundred times. As soon as you reach that conclusion, Applejack is thrown off the Mecha-Crab, and is forced to retreat back to the barn, leaving you to be chased around the farm for a good five minutes, before she returns with a plank of wood, a log, and several boulders. To launch at the exhaust ports.

Improvising a see-saw, the pair of you load up and prepare to fire. Applejack assures you that she's got a good eye, and won't miss: just point out the legs with the open exhaust ports, and she'll let the rocks fly. So hurry up! Which legs need to be attacked to bring the crab down?

Author's Note:

I dunno. Scale in Transformers is not something they cared about. In the eighties, particularly.

1. One hundred legs on the Crab-Apple-Mecha.
2. One strike from the Mecha opens all the ports in its legs.
3. The second strike closes all leg ports except every second leg port.
4. The third strike closes every third leg port if it's open, or opens it if it's closed.
5. The process continues until the crab hits the Mecha up to and including one hundred times.

PUZZLE: How many leg ports are still open after all that, and which ones?

Comments

[ANW]

Another Ted-ed problem.
The only exhaust ports that remains open are the ones that have an odd number of factors. And the only numbers that do so are perfect squares.
1,4,9,16,25,36,49,64,81,100.
Those are the legs we need to go after.

[Ri2]

Goddamit, Flim and Flam!