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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x^x)' = x^x + x^x\log(x)} . Why is the derivative the sum of the Prof's solutions?
Sept 14	Can all of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{R}^2} be covered by a set of disjoint, non-degenerate, circles? What about Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{R}^3} ? Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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? Hint (Hover)
Sept 23	Can you find uncountably many subsets of $\mathbb {N}$ s.t. the intersection of any two of them is finite?
Sept 26	In how many ways can you place 4 different points in the Euclidean plane, such that there are 2 different distances between all the points?
Sept 28	Can you find uncountably many subsets of $\mathbb {N}$ s.t. for any two of them A and B, (A $\subset$ B) or (B $\subset$ A)?
Sept 30