1617-257/Riddle Repository

Riddle Repository

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

Date of Lecture	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? 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	In a random 13-element subset of 1,2,...,52, what is the average value of the smallest element? (Credit: Yujia Yin)
Oct 3	A spherical loaf of bread is put in a bread cutting machine. Which slice gets the most crust?
Oct 5	Can you write the function $f(x,y)=1+xy+x^{2}y^{2}$ as $f(x,y)=\sum _{k=1}^{2}g_{k}(x)h_{k}(x)$? (Credit: Yujia Yin)
Oct 7	Prove: If you tile a rectangle (whose sides are not integers) with rectangles, at least one of those will have both sides non-integer.
Oct 10	(Thanksgiving holiday - University closed)
Oct 12	Players A and B alternate placing 1 x 2, 1 x 3, and 1 x 4 lego pieces (as they choose) on a 19 x 21 board, with no layering and no overlaps. If you cannot place a piece, you lose. Who would you rather be A or B? What if the overall size was 20 x 20?
Oct 14	No riddle. Discusses past riddle from Sept 19.
Oct 17	An ant walks at 1cm/sec along a super-rubber-band that stretches at 1m/sec. Will it ever reach the other end? Why not? How long will it take? (Credit: Kodiak Jackson)
Oct 19	How far can you go with n Jenga blocks?
Oct 21	Can you place 6 identical real-life Jenga blocks/chalks such that any two of the will touch each other?
Oct 24	Can you pack 125 1 x 2 x 4 boxes inside a 10 x 10 x 10 cube?
Oct 26	Can you pack 21 3 x 1 rectangles on an 8 x 8 board? Any constraints on where the missing piece would be?
Oct 28	No riddle.
Oct 31	A total of k kids share a loot of n indivisible candies. The first proposes a split. If not accepted by a strict majority, she leaves and the second proposes a split... etc. How will the loot be split?
Nov 2	Abhishek is at the centre of a circle of radius 100m. On the circle is a Lion. $V_{L}$ = $4V_{A}$. Help save Abhishek, by giving him a strategy that can always get him out of the circle, given that the Lion is very intelligent.
Nov 4	Dmitry is at the centre of a stadium of radius 100m without any exit. A Lion is also in the circle. $V_{D}$ = $V_{A}$. Given that Dmitry and the Lion are very intelligent, how long can Dmitry survive?	Hint: Can you find a sequence of points,so that the lion cannot catch Dmitry when he goes from one point to the next point, along the line connecting the two points? Clearly, if the distances of these line segments sum up to infinity, then Dmitry can run forever. -Yujia
Nov 7	(Fall reading break - No classes)
Nov 9	Can you find two irrational numbers x and y such that $x^{y}$ is a rational number?
Nov 14	Can you find a continuous f: [0,1] -> [0,1] with f(0) = 0 and f(1) = 1 which is differentiable with Df = 0 except on a set of measure 0?
Nov 16	Can you cover a diameter 100 disk with 99 (possibly overlapping) 100 x 1 bands?
Nov 18	No riddle.
Nov 21	n ants walking towards m ants on a wire. All of them have the same velocity. When any two ants meet, a bang is heard. How many bangs are heard all together?