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Private
1.1. Do you want to use primarily mobile or stationary laptop? How mobile should the laptop be? Should it be a 2-in-1 laptop / convertible?

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Mobile, in bed, in the kitchen, on the go and on vacation

1.2. If you want to play: what games? What level of detail?
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Starcraft 2, Counter Strike or maybe something Mortal Kombat together on the train with friends. The level of detail is sufficient: low.

1.3. Music / Image / Video Editing or CAD – Which Software? Professional or hobby?
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Not,
2. How big should the screen be? Would you like a touch screen or a particularly high quality of display?
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13 to 15 inches
3. How long should the battery last?
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as long as possible, of course. But it plays a small role.
4. What operating system do you want to use? Is there a license? Should the laptop already have an operating system pre-installed? Do you get Windows from college?
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Windows
5. Do you have any wishes regarding design, quality of workmanship, material, or color?
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The workmanship, of course, should be beautiful, it should not feel cheap.

6. Are there other special requirements that were not consulted? Big hard drive? Numeric keyboard? Keyboard backlight? Pen holder? Docking via USB-C / Thunderbolt 3? CD / DVD drive? Discounts (educational)? Service and warranty? Maintenance options? SD card reader?
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The numeric keypad is good but not essential.
For me it is simply important that the laptop does not have a fan. It should work silently.
This is also where the challenge lies. I can hardly imagine if there is a device that guarantees it.

7. How much money are you willing to spend? Is a used purchase an option?
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1000 to 2000 €
I have no idea if such a device exists. Especially with the specs.
But you can try.