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Magic Pumpkin - The 'singular' algorithm
Bà phù thủy có những chiếc đèn lồng bí ngô rất đẹp và cũng hoạt động rất khác thường. Làm sao bật hết các đèn lên đây?
This is one of the more advanced problem. I call this the absolute singular problem.
The reason is, you can try multiple times and light up all 7 pumpkins. But what if the Witch has an enormous number of lamps, let's say, 2020?
She will probably need a computer to automatically turn on all the lights in a scripted and certain algorithm. And I say, she can change the status (on/off) of each individual lamp without changing the status of ANY other lamp. This you may try to prove true for all number of lamps not divisible by 3.
That is why I call this type of problem "singular", because every variable has an independent status, no matter if the other lamps are on/off.
I would say it's not difficult to prove this, but how do we come up with changing the status of each lamp? After all, this is a STRONGER problem than the original one. There are two signals for this
1. All the variables are symmetric. In the case of this problem, all lamps are connected to two others, and lie on a circle, which makes them symmetric in terms of position.
2. The initial/ending position are random. This means any transformation can happen right? And if so, why cannot we change the status of only one variable?
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