Divisibility Rules

A divisibility rule is a shortcut you can use to see if an integer is evenly divisible by another integer, without doing the actual division. Most divisibility rules involve looking at the digits of the number. Here are some easy…

Vacant Room Probability

Your workplace has a phone room for employees to quietly make personal calls. The room has no windows, just a sign that can be switched from “Vacant” to “Occupied”. However, employees differ in how consistently they use the sign: 1/2…

Break the Cipher

The CIA is tracking a criminal organization and have reason to believe they are about to launch some sort of attack on New York City. One morning, they intercept this message, can you break the cipher and figure out what…

Random Turns

You are in a city with streets on a perfect grid – every street is north-south or east-west. You are are driving north, and decide to randomly turn left or right with equal probability at the next 10 intersections. After…

Water Jug Riddle

You have a 3-litre jug and a 5-litre jug, and as much water as you need. How do you measure out exactly 4 litres using only these two jugs? This is a classic logic puzzle, sometimes used in finance and…

Impossible Sudoku

You may be familiar with Sudoku, a combinatorial number placement puzzle in which you fill in a 9×9 grid with digits such that each row, column, and 3×3 square contains all of the digits 1-9 exactly once. You come across…

Berkson’s Paradox

Berkson’s Paradox is a counterintuitive or unexpected trend observed in a sample due to a particular type of selection bias. This bias arises when the sample is selected based on the combination of two characteristics. Also known as Berkson’s bias…