There are one hundred natural numbers, they are all different, and sum up to 5050. Can you find those numbers? Are they unique, or is there another bunch of such numbers?
Can \(100\) weights of masses \(1,2,3,\dots,99,100\) be arranged into \(10\) piles, all of different total masses, so that the heavier a pile is, the fewer weights it contains?
How many integers are there from 0 to 999999, in the decimal notation of which there are no two identical numbers next to each other?