The Infinite Chocolate Bar
A chocolate bar is cut into five pieces: a small square, a rectangle, two diagonal slope pieces, and a large base piece. We rearrange the pieces, reforming the...
Stack of Coins 3
Once more, you and your friend stumble on another pirate’s treasure: an old chest filled with coins: 575 copper coins and 1 gold coin. As before, these old...
Stack of Coins 2
You and your friend have decided to make treasure hunting your weekend project. After a few weeks of treasure hunting, you guys stumble on another pirate’s...
Stack of Coins 1C
You and your friend are really lucky treasure hunters, because you’ve stumbled on another pirate’s treasure: an old chest filled with coins: 149 copper coins...
Stack of Coins 1B
You and your friend stumble on another pirate’s treasure: 99 copper coins and 1 gold coin. As before, these old coins are no longer legal tender, so the copper...
Stack of Coins 1A
You and a friend stumble on a pirate’s treasure: an old chest filled with coins: 19 copper coins and 1 gold coin. These old coins are no longer legal tender,...
Vanishing Square
The diagrams below show two arrangements of the same four pieces. Both form a 13 by 5 right triangle. Yet the first arrangement contains a 1-square-unit gap,...
Jewel Thieves and a Stolen Gem
The Moonstone has been stolen. Police have three suspects under surveillance—three of the city’s most notorious jewel thieves—but no evidence to arrest any of...
Randomised Ice Cream
For Employee Day, your company is offering everyone free ice cream, and you somehow find yourself at the front of the queue. The vendor manning the ice cream...
The Harmonic Series
Consider the infinite sum: [Math: 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \cdots] This is called the harmonic series. Each term gets...
Coconuts and a Monkey 2
Five people are stranded on a deserted island. They gather a pile of coconuts for food, planning to divide them equally the next morning. However, during the...
Coconuts and a Monkey 1
Ten people are stranded on a deserted island. The gather a pile of coconuts for food, planning to divide them equally the next day. However, that night, one...
Brothers and Sisters I Have None
A man is looking at a photograph of someone. His friend asks who it is. The man replies, “Brothers and sisters, I have none. But that man’s father is my...
Ants on a Pole
You have a 1-metre pole with 99 ants placed at each 1-centimetre mark (1cm, 2cm, 3cm, … 99cm). Each ant faces towards the centre of the pole (at the 50cm...
L-Shaped Room
We have a room made out of 3 squares arranged in an L shape. Two people are placed randomly within it. What’s the probability that they can see each other?
Unfair Heads and Tails
Player A has n+1 fair coins, while player B has n fair coins. Both players flip all their coins simultaneously and count the number of heads. What is the...
Trailing Zeroes in 100!
How many trailing zeros does 100! have?
Antipodal Temperature
Assume the Earth is a perfect sphere. Show that at any given time, there exist two antipodal points (points on exact opposite sides of the Earth) with the same...
Antipodal Temperature and Pressure
Assume the earth is a perfect sphere. Show that at any given time, there exist two antipodal points (points on exact opposite sides of the Earth) with the same...
Complex Number Multiplication
Consider computing the product of two complex numbers (a + bi) and (c + di) . Using the standard method we learned in school, we get: [Math: (a + bi)(c + di) =...
Ant on a Rubber Band
A taut rubber band connects a wall to the back of a toy racecar 1 metre away. At time t = 0 , the racecar drives away from the wall at 1 metre per second,...
8 Queens
Can you place 8 queens on a chessboard so that no queen can capture any other queen? Recall that a queen can move any number of squares horizontally,...
9 Dots
You have 9 dots arranged in a 3×3 grid: Without lifting your pen, draw four straight lines that pass through all 9 dots.
Ant in a Cube
An ant is at one corner of a cube with side length 1. The exit is a tiny hole on the corner diagonally opposite the ant. What is the length of the shortest...
Pirates and Coins
Five pirates discover a treasure chest containing 100 gold coins. Being logical and ruthless pirates, they must decide how to divide the loot. They follow a...
Poisoned Wine
To celebrate a decade of his rule, the king is holding an extravagant feast, accompanied with 1000 bottles of wine. However, the day before the feast, he...
Poisoned Wine (Extension)
Before the king gets to administer the bottles of wine to the prisoners, an advisor stops him. He says that if more than 8 prisoners die, the townspeople might...
3-Bit Sensors
A remote weather station uses two redundant 3-bit sensors to measure atmospheric pressure. Both sensors transmit their readings to a central processor, but...
Planting Trees 3
The mathematics professor has become your most loyal client. After solving her first two challenges, she calls you back with what she claims is her hardest...
Planting Trees 2
A few weeks after your first job, the mathematics professor calls you back. She was so pleased with your creative solution to the four-tree problem that she...
Planting Trees 1
You are a landscape gardener working on a project for a mathematics professor. She has an unusual request: she wants you to plant four trees in her garden such...
Egg Dropping
For a school project, you’ve devised an egg-protection device — a little contraption that wraps around an egg and is supposed to keep it from breaking when...
Two Gloves and Three Patients
You’re a surgeon in a remote clinic when three patients arrive requiring emergency operations. Supplies are running low—you rummage through the stockroom but...
Dice Corner
You’re looking through a hole at the corner of a standard die. The image below shows all you can see through the hole: portions of three faces meeting at the...
Guessing Hats 3
The king’s challenges are growing crueller. This time, three wise men stand in a room, each wearing either a black or white hat chosen at random by a coin...
Guessing Hats 2
The king has grown tired of his wise men outwitting him. This time, he’s devised a more devious challenge. 10 wise men are lined up single file, all facing...
Coin Weighing 3
Your empire has grown even larger. Now 12 neighbouring kingdoms have each sent a single gold coin as tribute. Your advisor suspects that one coin is...
Coin Weighing 2
Your empire has grown, and now you receive tributes from 9 neighbouring kingdoms. Each kingdom sends a sack of gold coins as a gift. Your advisor suspects that...
Coin Weighing 1
You’re the king of a massive empire. As a gift, a neighbouring kingdom has sent you 9 gold coins. Your advisor suspects that one of the coins is a forgery —...
Equal Shape Cutting 4
With 1 cut, divide the zigzag shape into 2 equal shapes of itself. The cut does not have to be straight, but has to be a connected line. The shapes can be...
Equal Shape Cutting 3
Cut the trapezoid into 4 equal shapes of itself. The shapes can be rotated, but all 4 must be of the same size.
Equal Shape Cutting 2
Cut the L-shape into 4 equal shapes of itself. The shapes can be rotated, but all 4 must be of the same size.
Equal Shape Cutting 1
Cut the triangle into 4 equal shapes of itself. The shapes can be rotated, but all 4 must be of the same size.
Measuring Time with Hourglasses 3
As your cooking skills improve, you decide to try preparing baked salmon fillet. It needs to go into the oven for exactly 20 minutes. As before, you have two...
Measuring Time with Hourglasses 2
After your culinary experience with the soft-boiled eggs, you want to try your hand at cooking a steamed vegetable mix. This time, you need to steam your...
Measuring Time with Hourglasses 1
You’re making the perfect soft-boiled eggs: all you have to do is boil eggs in a pot of water for exactly 9 minutes. However, your kitchen timer is broken, and...
Chomp 4
After beating your friend at his game 3 times already, you wonder if there’s always a way to win for an n by m chocolate bar. As a reminder, here are the rules...
Chomp 3
Even after losing the previous 2 games to you, it appears that your friend has not yet learnt his lesson. This time, he has a rectangular chocolate bar made of...
Chomp 2
After winning the previous game, your friend is back for revenge. This time, he has a chocolate bar made of n by n squares. The same rules apply: You will take...
Chomp 1
You are playing a dangerous game with a friend. He pulls out a chocolate bar comprising 6 squares arranged in a 3 by 2 arrangement. The bottom-left square is...
100, 10, 1
Your friend, Cole, shows you his first attempt at programming: a calculator that takes in a binary sequence and does an arbitrary computation on it: If the...
Two Children 2
You’re talking to a different colleague at work when it comes up in the conversation that he has 2 children. “What genders are they?” you ask again. “Well, the...
Two Children 1
You’re talking to your colleague at work when it comes up in the conversation that he has 2 children. “What genders are they?” you ask. “Well, I have at least...
Two-Bullet Russian Roulette
After offending the toughest guy, Big Billy, at the saloon, he challenges you to a game of Russian Roulette. He takes out a revolver with 6 chambers and loads...
Fastest 3 in 25 Horses
You visit a farm, hoping to buy the 3 fastest horses they have. The farmer says he has 25 horses, but he has no idea how fast each of them are. Instead, he...
Chain Link 2
An apprentice is working for you, the village’s master blacksmith, for 21 days. For payment, you have agreed to give him a gold chain with 21 links, one link...
Chain Link 1
Five apprentices are working for you, the village’s master blacksmith. After three days of work, you now have to pay them each a gold chain of 3 links. You...
27 Cubes
A 9cm cube is to be cut into 27 smaller cubes, each of side length 3cm. This can be done with 6 straight cuts to the original cube: 2 parallel cuts along each...
The Keyboard Prank
Anne comes into the office to find that her co-workers had played a prank on her. The keycaps on her keyboard had been shuffled such that if she types out a...
One Less Than a Prime Squared
Show that p^2-1 is always a multiple of 24 if p is a prime that is bigger than 3.
Confused Bank Teller
When Dorothy went to cash in a cheque, the confused bank teller swapped the dollars and cents. He gave her dollars in place of cents, and cents in place of...
Watermelons Drying in The Sun
A farmer is proud of his newest feat: growing a 120 kg watermelon that he wants to enter in the farming contest next week. Using a special sensor, he detects...
Hummingbird
A train leaves Oakridge at 20 km/h, headed for Fairhaven. At the same time, another train leaves Fairhaven at 30 km/h, headed for Oakridge on the same track....
Close Shave with a Train
Alan is traversing a railway track that spans over a treacherous ravine. As he reaches \frac{3}{8} of the way across the track, he hears the whistle of a train...
The Camel Race
An aging sheikh, nearing the end of his life, decides to leave his vast fortune to one of his two sons. To determine the heir, he devises a strange contest...
Taking Pills
After falling ill, Josh sees a doctor and is prescribed some medication. He is to take 1 pill of Xenoril and 1 pill of Yvexol every 24 hours. The two pills...
Proving Rules on Cards
On the table are 4 cards, each one labelled “A”, “D”, “3”, and “6” respectively. You know that every card has a letter on one side and a number on the other. I...
Marble Pairs
You’re given a jar containing 100 marbles, each one coloured either black or white, and there is at least 1 marble of each colour. You notice that if you pick...
Counting Towns from a Tower
The evil king, no longer trusting his 2 wise men, wants to test their wisdom, so he locks them in a tall tower in the middle of his kingdom. One wise man is...
Two Girlfriends and Two Trains
Unfaithful Bob has two girlfriends Alice and Carol. Bob can take a train ride from the city’s train station to get to them. There is only 1 line going in both...
Traversing the Hypercube
Ossarion-429 is a multi-dimensional being travelling across hypercubes of various dimensions. Bored and having nothing else to do, he wonders to himself if...
Diagonals on a Cube
Two diagonal lines are drawn on a cube. What is the angle between these two lines?
Average Salaries 2
Back in [[puzzle ]], 12 employees came up with a method to find out their average salary without revealing their individual salaries to anyone. Here’s the...
Average Salaries 1
There’s a global pandemic going on, so everyone is working from home. During this time, 12 employees with similar roles wonder if there are any large salary...
Coins on a Table
You and a friend want to settle who is the smarter of you two with a game. The game is played on a circular table, with you and your friend taking turns to put...
Guessing Hats 1
Angry with his three wise men, the evil king subjects them to an impossible task: they’ll have to guess the colour of the hats on their heads. If any one of...
Covering a Chessboard 1
You’re given an 8x8 chessboard with 2 opposite corner tiles removed. You can place dominoes on the board, with each one covering exactly 2 adjacent tiles (you...