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* There are 51 ants sitting on top of a square table with side length of 1. If you have a square card with side 1/5, can you put your card at a position on the table to guarantee that the card encompasses at least 3 ants?
-* What is the minimum number of colors needed to paint the plane so no two points 1 unit apart share a color?
+* What is the minimum number of colors needed to paint the plane so that no two points 1 unit apart share a color?
* A bond prospectus states: “This bond will default if and only if its default cannot be proven in ZFC set theory.” What is the bond’s credit rating?
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* You’re on a game show with countably infinite doors. Behind one is a car; the rest have goats. After you pick a door, the host (who knows what’s behind all doors) opens all but one other door, revealing goats. Should you switch?
-* There is a regular die and a special invisible die. You know that regular die has integers 1 to 6, but don't know what's on the invisible dice. After tossing, I speak the sum of outcome of both die. It so happens that the outcome is an integer between 1 to 12, with equal probability (1/12 each). Can you guess what are the numbers printed on special invisible dice?
+* I have a regular die and a special invisible die. You know that regular die has integers 1 to 6, but don't know what's on the invisible dice. After tossing, I speak the sum of outcome of both die. It so happens that the outcome is an integer between 1 to 12, with equal probability (1/12 each). Can you guess what are the numbers printed on the special invisible die?
* Two witches make a nightly visit to an all-night coffee shop. Each arrives at a random time between 0:00 and 1:00. Each one of them stays for exactly 30 minutes. On any one given night, what is the probability that the witches will meet at the coffee shop?
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* A very innocent monkey throws a fair die. The monkey will eat as many bananas as are shown on the die, from 1 to 5. But if the die shows '6', the monkey will eat 5 bananas and throw the die again. This may continue indefinitely. What is the expected number of bananas the monkey will eat?
-* What is the expected number of coin tosses required to get n consecutive heads?
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+* What is the expected number of coin tosses required to get n consecutive heads?
+* On Monday, a fair coin is flipped. If it lands as heads, you are awoken on Tuesday and Wednesday. If it lands as tails, you are awoken on Thursday. Whenever you are awoken, you are given the opportunity to buy a call option expiring Friday for a particular security. You have access to relevant data up to Monday, but are not told what day it is when awoken, and after each awakening your memory of that awakening is erased. How should you determine whether to buy the option?
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