1617-257/Riddle Repository

Riddle Repository

A collection of the riddles posed at the beginning of each lecture

Date	Riddle	Solutions, Discussion, etc...
Sept 12	We want to compute $(x^{x})'$. Prof. A claims $(x^{n})'=nx^{n-1}$, so $(x^{x})'=xx^{x-1}=x^{x}$ Prof. B claims $(a^{x})'=a^{x}\log(a)$, so $(x^{x})'=x^{x}\log(x)$ Smart student says $(x^{x})'=x^{x}+x^{x}\log(x)$. Why is the derivative the sum of the Prof's solutions?
Sept 14	Can all of $\mathbb {R} ^{2}$ be covered by a set of disjoint, non-degenerate, circles? What about $\mathbb {R} ^{3}$? $\mathbb {R} ^{4}$?
Sept 16	Can you find uncountably many disjoint subsets of $\mathbb {R}$?
Sept 19	Can uncountably many Y shapes be fit into $\mathbb {R} ^{2}$
Sept 21	On any pair of potatoes, can you draw a pair of 3D congruent curves?
Sept 23	Can you find uncountably many subsets of $\mathbb {N}$ s.t. the intersection of any two of them is finite?