Question

Using mathematical induction to prove the following-;
If there are n participants in a knock out tournament then prove that (n-1) matches will be needed to declare the champion

Answer 1

induction eh.... the intuition is there, but how to "prove" it is fuzzy. I remember reading something about: taking a concrete example like n=3 and deducing that the rule follows from that example; then take another concrete example like n=5 and following it thru to the end,

then use k for the example, then conclude the results. proofs have never been my strong point :)

Answer 2

well we start with n = 2 and see that the proposition is true, mean if there are two players, only 1 match is needed

Answer 3

then suppose that it is true for n= k, meaning that if k players participate, we need k-1 matches, n using this supposition we show that the given proposition is true for k +1 players

Answer 4

uzma's got it ;)