@@ -3,2 +3,3 @@
* A bag contains N socks, some of which are black, and some of which are red. If two random socks are picked, the probability that they are both red is 1/2. What is the smallest possible value of N for which this is possible?
+* You shuffle a standard 52-card deck. What is the probability that the first ace appears exactly at the 20th card?
* For a 3 sets tennis game, would you bet on it finishing in 2 sets or 3 sets?
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* You're in a room with three light switches, each of which controls one of three light bulbs in the next room. You need to determine which switch controls which bulb. All lights are off to begin, and you can't see into one room from the other. You can inspect the other room only once. How can you find out which switches are connected to which bulbs? Is this possible?
+* Find the smallest multi-digit prime number that is a palindrome with an even number of digits.
* Two sentient dice adjust their faces after each roll. If you roll a 4, your die subtracts 1 from its faces; your opponent’s die adds 1. What’s the optimal strategy to maximize the expected sum over three rolls?
@@ -110,2 +112,3 @@
* 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?
+* In a repeated Prisoner’s Dilemma, what is the Nash equilibrium if both players use tit-for-tat strategies?
* A stick is broken into 3 parts, by choosing 2 points randomly along its length. With what probability can it form a triangle?