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The problem of the Hanoi Tower is a classic exercise in recursiveprogramming: the solution has a simple recursive definition, and its complexityand the matching lower bound are the solution of a simple recursive function(the solution is so easy that most students memorize it and regurgitate it atexams without truly understanding it). We describe how some very minor changesin the rules of the Hanoi Tower yield various increases of complexity in thesolution, so that they require a deeper analysis than the classical Hanoi Towerproblem while still yielding exponential solutions. In particular, we analyzethe problem fo the Bouncing Tower, where just changing the insertion andextraction position from the top to the middle of the tower results in asurprising increase of complexity in the solution: such a tower of $n$ diskscan be optimally moved in $\sqrt{3}^n$ moves for $n$ even (i.e. less than aHanoi Tower of same height), via $5$ recursive functions (or, equivalently, onerecursion function with $5$ states).

Bouncing Towers move faster than Hanoi Towers, but still require exponential time