I already have a proven claim to prove that a $2^n \times 2^n$ courtyard can be filled with L-shaped tiles with a centre tile available to install a statue (of a wealthy donor "Bill" in this half-true story).
Now, I am attempting the below problem (taken from free textbook: Mathematics for Computer Science textbook from MIT):
Where is the theorem wrong? Why doesn't the argument made in the first problem apply to the second one?
- I found the base case, OK.
- I was thinking whether the odd shape of the second problem would make building the inductive hypothesis difficult. But I cannot really see why the hypothesis as stated can be argued to be false.
- Is it the case that for this problem, a stronger hypothesis (which was necessary for solving first problem) is not a valid one?