The third problem of the classification problem: —– You may be familiar with the works of Alfred Lord Tennyson, the famous English poet. In this problem we will concern ourselves with Tennison, the less famous English tennis player. As you know, tennis is not so much a game of skill as a game of luck […]
Here’s the second problem of the qualification round: ———– A group of N high school students wants to play a basketball game. To divide themselves into two teams they first rank all the players in the following way: Players with a higher shot percentage are rated higher than players with a lower shot percentage. If […]
Here’s the first problem of the qualification round of the Facebook Hacker Cup 2014: You want to write an image detection system that is able to recognize different geometric shapes. In the first version of the system you settled with just being able to detect filled squares on a grid. You are given a grid […]
A random variable (also called stochastic variable) is a variable that can take a set of possible different values, each with its own probability. For example, the experiment could be picking a person at random, and a random variable would be the person’s height. A random variable can be discrete or continuous. Discrete random variables […]
I saw this problem in a Probability course offered by the Harvard Extension program. I highly recommend it if you have the time. Here’s the problem: In Solomon’s reign there were two types of prophets: true prophets, who spoke the truth 9 out of 10 times, and false prophets, who only spoke the truth 5 […]
The problem: Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows: 21 22 23 24 25 20 7 8 9 10 19 6 1 2 11 18 5 4 3 12 17 16 15 14 13 It can be verified that the sum of the numbers on the diagonals is […]
Before I explain what the prosecutor’s fallacy is, here’s a real life example where it affected (for the worse) the life of someone. Sally Clark was a British solicitor, and in 1996 his first son died, only weeks after his birth. In 1998 the same pattern occurred, when his second son died only weeks after […]
The problem: Euler discovered the remarkable quadratic formula: n² + n + 41 It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when […]
Thomas Bayes was an English minister and mathematician, and he became famous after his death when a colleague published his solution to the “inverse probability” problem. Described below. Given that you have a urn with 10 black balls and 20 white ones, what’s the probability that by picking randomly you’ll get a white ball? This […]
Below you’ll find the PHP code to make a simple POST request using cURL. You can send the POST request either to your own server/domain, or to an external one, though it’s not guaranteed the external host will accept your POST. <?php $name = "John Doe"; $email = "johndoe@hotmail.com"; $url = "http://www.domain.com/signup/"; $fields = "name=$name&email=$email"; […]