*2: Writing nothing is a valid party. Consider the following solitaire game: Tak
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*2: Writing nothing is a valid party.
Consider the following solitaire game: Take a piece of paper, and write as many distinct positive integers on it as you want. A move in this game consists of the following: Pick any positive integer k on the page. Erase it. Write as many new positive integers less than k on the page as you want^2 The only rule is that you cannot have any repeated positive integers on your page after you do this. Prove that no matter what you do, this game eventually ends: that is, that you cannot play forever.Explanation / Answer
if you consider a large number n= 9 and erase it then you can write n-1 positive integers ( no repetition allowed) but note that there is no boundation for n-1 numbers I mean " you can write number from 1 to 8 or 8 or, 1 & 2 & so on" . like if you write 2 in the paper then you have one choice left that is 1 hence games complete because all the above conditions are satisfied. So, In general, we can say that we can say that if we write any positive integer "k" then we have k-1 positive integers are available to complete this game. hence this implies that no matter what we do, this game eventually ends.
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