The n citizens of a small community devise a strategy which they think might divide up work evenly between men and women. There are projects that they are considering doing, numbered 1, 2, …, m. Each person is to identify a subset of those projects as important. These subsets (A1, A2, …, An) do not need to be distinct or disjoint. Then, the women will take responsibility for the projects which are identified as important by an odd number of people, and the men ... see more at expii.
The landline telephone network was designed for 99.999% reliability. To get an idea of how strong that is, suppose you have a game of “telephone” consisting of a chain of 100,000 people. The 1st person receives a message from outside, and repeats it to the 2nd person, who then repeats the message to the 3rd person, and so on, until the 100,000th person receives the message. See more at Expii.
You are attending a Thanksgiving dinner party, where there are 13 people in total. You observe the patterns of existing acquaintances between the people, looking for triangles (sets of 3 people, for which all of the 3 pairs of acquaintances were present) and anti-triangles (sets of 3 people, for which all of the 3 pairs of acquaintances were not present). What is the minimum total number of triangles and anti-triangles that you could possibly observe?
Consider two societies, each with an extreme form of leadership overseeing 1 million people. Each society is modeled as a group of people marching together on a two-dimensional flat surface. In each society, each person independently has a random direction that they prefer to walk in. (Any direction is permissible, not just North, South, East, and West.) ... See more at Expii.
Before the 15th Amendment was passed in 1919, women had to rely on men to represent them in the voting booth. Suppose that in a town, half the voting-age public are women and half are men, but only men can vote. On a particular issue of importance to women, 40% of the men are in favor and 60% of the men are opposed. If women were able to vote, and all of them voted in favor, what percent of the vote would be in favor?
Every morning, you take a bus to the subway station and then take a subway train to work. The bus and train rides each take 15 minutes, the bus runs every 15 minutes, and the train runs every 10 minutes. Due to traffic, the schedules aren’t synced, and so every day they’re offset from each other by a random amount. Today you start the journey at 7:45am, and need to make it to work by 8:30am. What’s the probability that you’ll make it on time, rounded to the nearest percent?
Facebook News Feed History of the World: Protestant Reformation Through Queen Elizabeth I
Collaboration is very powerful! Suppose you have a group of F students, each of whom independently has 55% chance of correctly answering each true/false question on a test with 25 questions. Unfortunately, unlike the first puzzle, this time they don’t know whether they know or don’t know each answer. What is the minimum number of students which is sufficient to collaborate on the test, so that there is a strategy which results in them achieving an A ... See more @ Expii.
The American Music Awards are a regular fan favorite since the fans get to vote for the artists they want to win. This year Ariana Grande won Artist of the Year, which isn’t surprising since she is the 3rd-most followed celebrity on Instagram. Out of the 10 nominees, several appear on the list of accounts with the most Instagram followers. 2 of the other top 4 accounts with the most followers are listed below. If ranked, which one of her fellow nominees did Ariana Grande just surpass?