1617-257/Riddle Repository
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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 [math]\displaystyle{ (x^x)' }[/math].
Prof. A claims [math]\displaystyle{ (x^n)'=nx^{n-1} }[/math], so [math]\displaystyle{ (x^x)' = xx^{x-1} = x^x }[/math] Prof. B claims [math]\displaystyle{ (a^x)' = a^x\log(a) }[/math], so [math]\displaystyle{ (x^x)' = x^x\log(x) }[/math] Smart student says [math]\displaystyle{ (x^x)' = x^x + x^x\log(x) }[/math]. Why is the derivative the sum of the Prof's solutions? |
|
| Sept 14 | Can all of [math]\displaystyle{ \mathbb{R}^2 }[/math] be covered by a set of disjoint, non-degenerate, circles? What about [math]\displaystyle{ \mathbb{R}^3 }[/math]? [math]\displaystyle{ \mathbb{R}^4 }[/math]? | |
| Sept 16 | Can you find uncountably many disjoint subsets of [math]\displaystyle{ \mathbb{R} }[/math]? | |
| Sept 19 | Can uncountably many Y shapes be fit into [math]\displaystyle{ \mathbb{R}^2 }[/math] | |
| 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 [math]\displaystyle{ \mathbb{N} }[/math] s.t. the intersection of any two of them is finite? |
