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+-SH safe2281400 +-SH twilight sparkle371681 +-SH alicorn336913 +-SH pony1711364 +-SH g42123545 +-SH my little pony: friendship is magic269077 +-SH princess spike796 +-SH 4chan7066 +-SH anonymous725 +-SH arial72 +-SH book46038 +-SH bronybait3494 +-SH comment bait25 +-SH cute280350 +-SH dream3449 +-SH female1912240 +-SH if you see this image while scrolling15 +-SH mare814176 +-SH meme97410 +-SH sleeping30777 +-SH tired4761 +-SH twilight sparkle (alicorn)155292
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SLEEP TIGHT, TWILIE
SLEEP TIGHT TWILIE
…aah…
@Cirrus Light
@Cirrus Light
K N O W L E D G E
@Cirrus Light
NEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEERRRRRRRRRRRRRRD
If you imagine there’s a three-character window, and you have a repeating string of ABCABCABCABCABC…, then you can scroll it three places to the right to get all possible combinations. Watch the “A”:
ABC
CAB
BCA
ABC
The fourth is a duplicate, so there is three unique combinations.
In order to actually change the ABC string instead of merely “sliding” the ABCABCABC… to the right or left, we have to change the intrinsic order. ACB accomplishes this. As illustrated above, CAB, for example, would not. But because A has B to its right, the ABC pattern will never produce ACB, therefore, it is a unique combination.
Let’s look at the possible “windows” of ACB repeating (ACBACBACBACB…)
ACB
BAC
CBA
ACB
The fourth is a duplicate, so there is three.
You can only uniquely change the order once, though. Notice that trying to change the order again will simply give you a combination of ABC.
ACB. Switch B and C: ABC. Switch A and C: CAB. Switch A and B: BCA.
This is because we’ve set the set up to repeat - ABCABCABC… - so selections of the ABCABCABC set correspond to a mere shift that doesn’t actually change the intrinsic properties of the set itself.
The intrinsic properties are the relationships in-between the three letters. Because there are three letters, we can completely define this string by two relationships:
ABC
After an “A”, place B. After a “B”, place “C”.
These instructions are the relationships in-between the three letters. Notice, we can only swap the instructions once:
After an “A”, place C. After a “C”, place “B”.
This is because of how the instructions are structured. In part 1, we specify after what letter, and then we command another letter to be placed that is not the first letter. Since there are only three, that letter must be either C or B - only 2 options. Once you have made this choice, the next instruction is complete defined: it must tell you what to do next, so it says “After” [whatever letter you picked to place in the first instruction], place [the only letter not yet used].
And so with the constraints that every letter must be used exactly once and there’s three letters, this means you can only change the order of the letters once - that single swap that’s mentioned - since there are only two options for what to place first, and after choosing one option, the rest of the instructions are unavoidably set with no possible further choices.
…
…This is what happens when I stay up too late.
Haha, it’s 3:14. Pi…
…
Hmmm…
ABC
CAB
BCA
CBA
ACB
BAC
3 * 2 * 1 words = 6 possible combinations, so that’s all of them. (This is awesome!)
So that’s
Sleep tight, Twilie. (A = Sleep, B = tight, C = Twilie)
Twilie, sleep tight. (Oooh, it works!)
Tight Twilie, sleep.
Twilie, tight sleep.
Sleep Twilie, tight.
Tight sleep, Twilie.
:D
The Twilight-Pinkie fusion would be proud :p