1617-257/Riddle Repository: Difference between revisions

Revision as of 12:43, 22 September 2016

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

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 |Sept 12
+|We want to compute <math>(x^x)'</math>.
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+Prof. A claims <math>(x^n)'=nx^{n-1}</math>, so <math>(x^x)' = xx^{x-1} = x^x</math>
+Prof. B claims <math> (a^x)' = a^x\log(a)</math>, so <math>(x^x)' = x^x\log(x)</math>
+Smart student says <math>(x^x)' =  x^x + x^x\log(x)</math>. ''Why is the derivative the sum of the Prof's solutions?''
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 |Sept 14
-| Can all of <math>\mathbb{R}^3</math> be covered by a set of disjoint, non-degenerate, circles?
+| Can all of <math>\mathbb{R}^2</math> be covered by a set of disjoint, non-degenerate, circles? What about <math>\mathbb{R}^3</math>? <math>\mathbb{R}^4</math>?
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