Triangle On A Circle
A triangle is generated by three random points on the unit circle. What are the odds it contains the circle’s center? The same in 3D - for the unit ball...
Riddles
I love math/CS/physics riddles. This list contain those I consider the best I have encountered. Some of them (I found out afterwards) are so famous they have their own Wiki page.
Stock Price
A stock starts trading at a price of 1000 at the first day. Each day it can either go up or down 1 point. What are the chances that in the 1000 day it will r...
Stacked Slabs
You need to stack slabs one on top of the other and maximize the horizontal distance. What is the maximal distance you can reach without collapsing if the le...
Playing With Keys
You walk down the street, throw your keys in the air and catch them. Do the keys spend more time going up or down?
Jumping Frogs
Four frogs sit on integral discrete lattice at points (0,0), (0,1), (1,0) and (1,1) and form a square of length 1. Each frog can make a mirror jump over any ...
Hot Water
You are trying to boil a liter of water in your pot and you happen to have a glass of water in 95 degrees Celsius. Should you poor the glass into the pot?
Good Batteries
You are given 8 batteries, 4 of which are full and 4 empty, and a kids’ toy that needs two batteries to start working. You have maximum 7 trials to get the t...
Game Of Life
In Conway’s Game of Life with these rules: Only 4 neighbors. Create new if two or more neighbors exist. Cannot die.
Dobble
Dobble is a vary nice speed matching game I played with my kids. The first time I saw it I was amazed by the math here so I decided to “turn” it into a riddl...
Climbing Monkeys
Two identical monkeys are hanging on a rope through a pulley. What would happen if one of them started climbing on the rope (originally presented by Lewis Ca...
Carrying a Log
Three man carry a log. Assuming they are all the same height, who carries the most weight?
4 Digit Code
You need to unlock a 4-digit code with no “enter” button. What is the minimum number of presses you need? In other words, you need to generate the shortest s...
13 Balls
We are given 13 balls and told that for any subgroup of 12 balls they can be divided into two subgroups of 6 balls that have the same weight. Prove that all ...
117 Segments
You are given 117 segments with integer length. Prove that there is a subset of them that is divisible by 117.
Feynman’s Restaurant Problem
Quoting from the Feynman Lectures (Exercises -> Feynman’s restaurant problem):
Two Envelopes Problem
Quoting from the wikipedia:
The Three Hat Problem
Quoting from the source:
Poisoned Bottles
You are given 1000 bottles, one of which is poisoned, and as many mice as you want. You can tell any mouse to drink from some bottles as you decide. If a mou...
Secretary Problem
Quoting from wikipedia:
Josephus problem
N people stand in a circle and are numbered 1 to N. Starting from the first person, we skip him and shoot the next one, then we skip 3 and shoot person 4. we...
Underground Cable
You are given a 1km x 1km square area and you are told there is a straight line of cable hidden 1 meter below the ground that passes somewhere through this a...
Them apples
You have 3000 apples in point A and you want to move as much as you can to point B which is 1000 KMs away. the truck’s capacity is 1000 apples and the driver...
Singly Linked-list
Given a unidirectional Linked-list: Find if it has a loop Find the loop’s length Find the junction node
Points on the Plane
Given 1000 green points and 1000 red points on the plane, show that we can draw 1000 straight lines between red and green points such that the lines don’t in...
Manhattan Distance
Imagine a grid on the plane (like Manhattan’s streets). You and your friends live on the junctions. (maybe some of you live in the same building):
Cards Magic
You are given a regular deck of 52 cards. A magician enters the room and tells you to choose 5 cards as you wish and lay them on the table face up. Then he t...
Array of length N+1
Given an array of length N+1, containing values from 1 to N, find a value that occurs at least twice in O(N) complexity and O(1) space. You cannot change the...
A Room with 4 bits
There are 4 random bits in a room.
100 Numbers
100 people get hats with numbers between 1 to 100 (there can be duplicate numbers). Everyone can see all numbers but their own. Each one gets a chance to gue...
100 Boxes
There are 100 boxes in a room that contain the numbers 1-100 (in some permutation). Two people will enter the room. First one can switch the content of two b...