My cat is getting extremely naughty !

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Hello friends, My new cat Koni is just few weeks old. She is getting bigger day by day and also getting very impatient. I usually find cats very lazy as they like to sleep most of the time but she is very very active. My house is in the 3rd floor and Koni likes to jump from the stairs. She is very keen to go down jumping and then climb it again. I don't know what fun she gets out of it but she likes to do it a lot. Also she tries to nail the door with her claws in a very awkward standing position. I'm worried that she might hurt herself someday doing all these exercise. I don't want to tie her or keep her in a closed room as they should be kept free in my opinion. But I think she might get into problems if she keeps doing these stunts. So friends what should I do to refrain her from all these stunts and also if u got a cat what it likes to do? A friend of mine suggested me to give her some toys and a ball to play with Is it going to help? Cheers, Tutul