Homework Answers
Base
Case: n = 2
A1 and A2 are the teams. Put the winner first.
Inductive
Hypothesis: n = k
Assume that it works and all the k teams which are ordered 1, 2,
... k-1
Induction Case: Proving for n = k + 1
3 parts are there: New team is X
X beats the first team, then put the X at first
X lost to the last team, then put the X at last
X lost to team M that belongs to {1, 2, 3, ... k-1}. Then put the X
after M.
So, in any of the cases, we can still arrange them.
Hence Proved
--------------------------------------
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