How big a mirror do you need to be able to see all your body, and what happens to the size of your reflection if you back away from a mirror? Also, what is the Venus Effect? |

How to efficiently order lists based on popularity and recency. | |

Serial and Parallel bulb puzzle How to connect two bulbs in series or parallel with a switch. | |

The psychology of why people love to play slot machines. |

What is the relationship between the percentage overlap during an eclipse, and the separation of the objects? | |

How many miles to the gallon does a person get? |

Based on your skill, what is the probability of winning a tennis match? |

Grazing and Calculus Revisited Revisiting the optimal grazing field size using a barn and straight section fencing. | |

Simple physics simulations of cloth and rag-dolls based on Verlet Integration. | |

Why do companies not understand how poor customer service, whilst seemingly advantageous in the short term, is damaging in the long term? |

How can you determine Lucy`s secret number when you only overhear part of her conversation? |

The clever technology around how analog TV protocols were created, and why there was an odd number of lines on an old TV screen. |

How to turn water into wine (with and without recursion). Calculating Levenshtein distances. | |

What is the probability of pulling out matching pairs of socks from a drawer in darkness? | |

Compound interest and retirement Why it is critically important to start saving for your retirement as soon as possible. | |

Arrange the digits 1-9 to make a nine digit number such that the first digit is divisible by one, the first two divisible by two, first three divisible by three … | |

The mathematics of tape machines, cassettes, and toilet rolls. |

A classic problem about how to calculate the shortest crease by folding the corner of a piece of paper (and how most calculus text books get this wrong). | |

Notes from the show this year. |

The basics of linked lists. |

Incremental means and variances How to keep a rolling track of the average and standard deviation of a stream of numbers, without having to reprocess the entire set, and minimize the chance of precision loss. | |

Linear Feedback Shift Registers Incredibly useful, and efficient, ways to cycle through a range of values. |

What strategy should you employ when faced with a series of parallel experiments that have unknown outcomes? |

GoDaddy took one of my websites offline for six months, and only offered compensation of one month of future hosting costs if I were to renew! | |

The jet plane that shot itself down The unfortunate incident of the plane that shot itself down. | |

Colouring sets so there are limited arithmetic progressions. |

What is the area of the shaded quadrilateral? | |

How much energy can we extract from wind? |

Who is nearest the ball? | |

Mapping nearest locations. |

How to determine the contents of a treat bag with a single question. | |

A cryptogram puzzle using the digits 1-9. | |

Vestigial trigonometry functions Trig functions that were popular 30+ years ago, but are rarely mentioned these days. | |

A puzzle to determine the better strategy to hunt for Easter Eggs in sealed boxes. |

Online interactive hangman solver. | |

What is the optimal strategy for playing the Big Wheel? | |

Why do time estimates on progress bars sometimes go crazy? |

How does Carbon-14 dating work? | |

Centroids of semicircles and hemispheres How to calculate the centroid of a semicircle, and how this is different from a hemisphere. | |

Will self-driving cars enable jerks? Will laws have to change? | |

Notes and thoughts from my visit to CES 2017. | |

A classic puzzle involving cutting a painted cube into smaller cubes. | |

Analysis of the odds on this classic casino game. |

How do poker odds change with the addition of wild cards? | |

What is the relationship between the chances of a poker hand occuring and its rank? | |

Why do wire gauge numbers go up as wires get thinner? |

What is the optimal way to bend a flat sheet to make an efficient gutter? |

What orientation will a square log float in water? | |

What happens when you compress the space that is inside atoms? |

Blending independent estimates How should you combine two independent estimates of age (with different Variances)? | |

Why are the black and white keys of a piano spaced the way they are? | |

Bisecting an arbitrary triangular cake An extension of the cake cutting puzzle from last week. | |

What is shortest cut on a triangular cake to make two equal sized pieces? |

Detecting (and correcting) errors in digital signals. | |

Defective Circuit Board Puzzle I have ten circuit boards, and I know exactly two are bad. | |

Consumer Electronics Show 2016. | |

Generating snowflakes using recursion. |

The World's hardest, easy, geometry puzzle? | |

Will future digital computers move away from binary? | |

Can you estimate the number of unfound errors in a document by comparing two independant analyses? |

Generating mazes with back track recursion. | |

How much does the addition of dimples adjust the Volume and Surface Area of golf balls? |

Why are the push buttons on a telephone arranged the way they are? | |

Chicken nugget numbers, and how to make optimal change. | |

Carnival of Mathematics blog-roll, episode 125. |

Congruent Rectangles Puzzle (trig solution) A trigonometric solution to last weeks geometry puzzle. | |

Congruent Rectangles in a Square Puzzle A geometry puzzle that, at first glance, appears to have not enough information to solve. | |

Obfuscation of text by shifting characters and simple substitution ciphers. | |

If you are trying to cool down a room with a fan, is it better to suck or blow air? | |

I'm climbing the Seattle Space Needle to raise money for cancer research. | |

Why are the numbers on a roulette wheel distributed the way they are? |

Calculating Pi by dropping needles onto a floor covered by parallel lines. | |

A million dollar math puzzle, and some pretty pictures. | |

What is the area of the region formed by the overlap of four semi-circles in a square? | |

The geometry of running tracks Why are running tracks oval in shape, and why do runners start from staggered positions? |

Geometry Puzzle (alternative solution using trigonometry) An alternative solution to the puzzle from last week solved using trigonometry. | |

Geometry Puzzle: Inscribed rectangles and equilateral triangles What are the dimensions of an inscribed rectangle that has the same area as an inscribed equilateral triangle? | |

How deep was the Deepwater Horizon drill when the accident happened? | |

How much money do bloggers make? An honest disclosure of the money I make from blogging? Is it possible to make a full time living from just blogging? | |

Can you save money by refuelling when it is colder out? Is it better to purchase gas when it is cold outside? How much difference does the temperature make to the volume of gasoline pumped? | |

Lissajou curves - pretty pictures from sine waves Pretty pictures generated from the orthogonal combination of sine waves of different frequencies and phase. | |

Three tools to help with the solving and generation of anagram puzzles. |

What is the optimal shape for a bucket? Mathematically, what is the optimal shape to make a bucket so that it holds the greatest amout of fluid for the amount of material used? | |

Consumer Electronics Show 2015 Notes from my annual pilgrimage to the Consumer Electronics Show. | |

Is there a correct strategy for playing Deal-or-no-deal, and what does this teach us about risk tolerance? |

Classic 100 Prisoner Escape puzzle One hundred prisoners and one hundred boxes. They can all be set free if they are able to find their own numbers. | |

If you select a dealer by the first person to receive an ace, how biased is this? | |

How much do clouds weigh, or do they float weightless? | |

Prison escape puzzle involving a chessboard and coins Using binary mathematics to solve, what seems like, an impossible puzzle. Is it possible to encode six bits of infomration with the flip of a single coin? |

Good and bad shuffling algorithms Have you been writing bad shuffling code your entire life? | |

Gray codes (also know as Reflected Binary Codes). Why are they so useful? | |

If every iPad was combined into one giant device, what would it look like? Apple have sold over 225 Million iPads. If these were combined into a single device, how big would it be? | |

Minimizing cross bracing in rectangular grids What is the minimum number of cross-braces needed to make a rectangular grid stable? |

Red/Black gambling game: Drawing cards from a shuffled deck If you draw cards from a shuffled deck, earning $1 for every black card turned over, and losing $1 for every red card, when should you stop? | |

Langford's sequences - arranging pairs of numbers with distinct gaps Arranging pairs of numbers into sequences so that there is a distinct separation between each pair. | |

If you ultimately win a soccer game, what is the probability you were always ahead? At the final whistle, if you win a soccer game, what is the probability you were winning throughout the entire game? | |

Why are volcanoes and sand dunes shaped the way they are? Why are many volcanoes and sand dunes shaped the way they are? |

If you shine a laser through a tray of cubed Jello, how many get bisected? What is the relationship between displacement and the number of edges crossed? | |

What is the best place to let go of a rope swing to go the furthest? What is the optimal strategy, when swinging on a rope, for letting go to maximize the distance you'll travel? | |

What would combining all the Worlds flags look like? If we combined all the flags in the World, would would the result look like? | |

Message in a bottle:Send and receive one time fortune cookies to random people. Someone, somewhere in the World will receive a message you write. You'll have no idea who gets it, and they will have no idea who sent it. Think of it like a giant game of fortune cookie. | |

Lowest Distinct Number auction game Guess a number with lots of other people and try to guess the lowest unique value. |

Tool for helping solve the word rounds in the Countdown game show. Dynamically type letters and see the longest words possible being built. | |

Solver for Countdown numbers game. Input the numbers and the target score and the optimal answer (or nearest possible) will be displayed. | |

Countdown numbers game. One of the oldest game shows on TV Analytics, history and rules of the Countdown numbers game. | |

How modern missile guidance systems work The evolution of missile guidance systems, from simple to sophisticated. | |

Why are cans made the size and shape they are? What is the optimal shape for a can to maximize the volume of food it can contain for the material used? |

Why are ice cream cones shaped the way they are? What is the shape of a cone that can contain the largest spherical ball of icecream for the minimum amount of cone material? | |

What symbol is scribed on Archimedes' tomb, and why? What is the ratio of the volume of a sphere to the volume of a cylinder? | |

What is the largest volume cylinder it is possible to carve from a solid sphere? What is the highest achievable ratio of the volume of a cylinder to the volume of a donor sphere? | |

Bad Hash: Random trivia about using the substitution cypher A=1, B=2 … What words are equivalent if we score the letters and add them? |

The best way to cut various numbers of circular pie crusts from squares of pastry What is the optimal way to pack circles in square? What is the optimal way to pack spheres in a box? | |

21 Bite-sized puzzles just hard enough to be solved over a good cup of coffee Coffee time challenge puzzles. Not too hard, but not too easy. Each should be solvable over a nice cup of tea or coffee. | |

Confidence levels, sampling, marbles, and Greek urns If you sample marbles from an urn, what can you learn about the urns contents? |

Greatest Hits - The top ten most read articles on my blog (by year) The most popular articles on my blog per year. | |

What is my motivation to blog? What tools do I use to create the graphics, charts and layouts? | |

Amidakuji - How to shuffle items and run lotteries using just a pen and paper Popular in Asia. How to run a 'random' lottery to distribute prizes using just a pen an paper. | |

Friday the 13th is more lucky than you think Did you know that the 13th of any month is more likely to a Friday than any other day of the week? | |

Detecting targets in noisy radar signals By comparing different samples it's possible to find things that stay the same and things that change. | |

Escaping from a pack of angry, laser toting, monsters using a holographic replicator What are your chances of escaping a monster using a device that makes replicas of yourself? |

Calculating geometric means in SQL, and why widescreen TV format is 16:9 There is no aggregate function in SQL to calcuate geometric means. How can you do it? Also, find out the relationship between geometric means and widescreen TV aspect ratios. | |

What is the lowest possible score in a game of Jeopardy? If you are really, really bad ae Jeopardy!, what is the lowest theoretical score you could achieve? | |

Compound Interest: How long does it take to double your money, and just what is 'The rule of 72'? The most powerful force in the Universe is compound interest - Albert Einstein. | |

Fuel consumption: Gallons per mile, or miles per gallon? Why it is more approprite to measure fuel comsumption in gallons per mile, not miles per gallon. |

Why are loops on roller coasters shaped like inverted tear-drops? Have you noticed that roller coaster loops all look similar in shape. Why is this? | |

Roller coasters, Moby Dick, Ski-jumps and accurate clocks (Brachistochrones) What is the quickest (not the shortest) path between two vertically seperated points? | |

Counting marathon runners and spying on WWII German tank production Estimating the total number of tanks an army has using a smaller observed sample. | |

Bounding rectangles, convex hulls, bullet holes and video games How to calculate the smallest area rectangle that encloses a collection of points. |

Can you lose weight by drinking iced water? If you drink cold water, your body has to warm it up to body temperature. How much energy does this take? Enough to be useful as a weight-loss system? | |

The fallacy of 'The Gambler's Fallacy' There is no such thing as the conservation of luck. | |

Newton and Pepys - A 300 year old probability puzzle A classic probability puzzle from history. |

How pressure changes with altitude Air is a fluid. Our atmosphere is denser at the bottom than the top. | |

Notes from my annual pilgrimage to the Consumer Electronics Show. | |

How to escape from a monster in a dark room A silly problem involving chasing after a rat in a totally dark room when the rat runs in a random direction. | |

How to hide from a laser wielding monster using a Corinthian column A silly problem about how to stay safe by keeping a column between you and a laser wielding monster. |

Mind reading trick - predicting magic symbols The computer will read your mind. Can you see how it works? | |

Mind reading trick - making cards disappear Think of a card, and the computer will make is vanish. Can you find out how it works? | |

Pixel scalers. How to rescale bitmap images Clever ways to scale up pixel art as resolution increases. | |

Why do pipes burst the way they do? Why is that pipes always burst along a seam, like sausages? | |

The difference between risk and uncertainty What's the difference between knowing the distribution of probabilities and not knowing the distribution? |

I don't want a smartwatch. I want a dumbwatch! Smart watches should be extenders, not devices in their own right. | |

Visual Cryptography - Create perfect secret messages you can see with just your eyes Methods to store hidden information using just the interference of images before the eye. | |

How to avoid being turned into monster soup! The Josephus problem. | |

QR Codes - How do they work, and how much can you damage them and still have them work? How far can you distort QR codes, and still use them? |

De Bruijn Sequences - What does DNA sequencing and guessing passwords have in common? Efficient ways of running through all possible permutations of a pattern. | |

How to escape a monster (using calculus) If you're trapped in a circular lake in a rowing boat, and there is a faster monster on the edge of the lake, how do you escape? (It could happen, and Calculus is your friend). |

Privacy is dead. Long live Trust! Debating about privacy is the wrong thing. We really should be talking about trust. | |

Is it quicker to walk backwards and forward along a travelator, or to one side? The answer might surprise you, and this has consequences for other situations. | |

Microsoft, this is what you need to do to save Windows Surface. It's a chicken and egg problem. To get over the energy barrier, you need to open your wallet. Large incentives are needed. |

YubiKey, Dual-factor authentication, and ModHex words fcddtegtheubdiidclkjiuijrbkducjj ilndfhilcrveineihbuvgjijbtfidrku ctndjtllgkhjkbkcdeufeiibvlfiftnu | |

How to elegantly rotate images How to rotate images using just shearing and scaling. | |

Why good customer service is so important to business success I don't understand how some services just don't get it. Today, great customer service is essential for success. | |

How are best-fit lines calculated? How linear regression works. |

Parity, disk drives, and how credit card numbers work Why do credit card numbers look the way they do? | |

Usain Bolt, the World's fastest man. How does he do it? If Usain ran at top speed over the entire 100m sprint, theroetically, what would his time be? | |

Exact Percentages, Simplifying Fractions, Prime Factors and Greatest Common Divisors When you see exact percentages quoted, can you infer anything about the sample size? | |

How much do you spend in a lifetime on coffee? When you sit down and calculate it, it's probably more than you think. |

TEDx Seattle: Photos, thanks and thoughts from the big day Pictures from the big day, and a link to the video. | |

Pulling random silver and gold coins out of treasure chests (and mischievous pixies) A simple logic puzzle. | |

My Speaking engagement at TEDx Seattle A humbling and exciting experience. | |

Selecting a random person (fairly) from an unknown number of applicants How do you select something randomly (fairly) when you have no idea of the total number of items? | |

The sincerest form of flattery? Impersonated accounts in Twitter My Twitter account was duplicated and impersonated. Here is a log of the process I followed to have the bogus accounts removed. | |

Triple A - Words with three letter A's and no other vowels There's more than you might think. | |

Why do sausages split like they do? Sausages seem to always split lengthwise. What is the science behind this? | |

Sicherman Dice (and how to cheat at craps!) Making a pair of dice that produce the same sum as two regular dice, but with different dot patterns. |

How hungover can you get? Kids blocks and Calculus! Is it possible to stack blocks overhanging from a table edge so that both edges of the top block are past the edge of the table? | |

How many words can you name that use each of the vowels once, and only once? | |

Turn an asteroid into a steroid with a broken keyboard If certain letters of your keyboard don't work, what alternative words can get created that will pass a spell checker? |

Solving Snake, the classic video game If you had to write an algorithm to completely solve snake, what would you do? | |

Old MacDonald had a Perihelion E-I-E-I-O. What words contain vowels in the order? | |

How do Roman Numeral lengths change with size? | |

To understand recursion, you must first understand recursion. Here recursion is used to solve a common coding interview question. |

If you always played the same symbol in a competition with other people who did the same, how does the number of people playing adjust your chances of winning? | |

l33t speak words (Hex words part 2) Words made by a combination of twister letters and numbers (geeky and popular with hackers). | |

You, me, and dead people (Hex words part 1) If you, me and DEAD people can read hexadecimal numbers, how many people is that in total? | |

Hilbert Curves - fractal spacing filling fun Self similar shapes with interesting practical properties. | |

Growing words, one letter at a time Start with a word. Add a letter to make a new word, then add another letter. How long a chain can you make? |

Consumer Electronics Show 2013 Notes from my annual pilgrimage to the Consumer Electronics Show. | |

Atomic typos - switching adjacent letters UNCLEAR NUCLEAR. Typos formed by the switching of two adjacent letters that result in another word being formed. | |

Wheel of Fortune puzzle solver - Win Big! Tools to help you solve Wheel of Fortune puzzles. | |

Random or Magic? Can you fool a computer at generating random numbers? How random are you? Maybe you are more predictable than you think? Try to create a random string of letters, then do the same by flipping a coin. Can the computer guess which is which? |

Trivial Wheel of Fortune bonus round - how lucky could you get? What words would be revealed totally in the bonus round without any letters being selected? | |

Are you worth more in dimes, quarters or nickels? What is the weight specific value of coinage? | |

How to mathematically select the best wife (or husband, or secretary …) If you are interviewing a know number of candidates and have to make a decission after each one, with no return, what is the optimal strategy? | |

Do you rename your digital photos? Does IMG_0001.JPG sound familiar to you? How often do people rename their photos? | |

Elemental Words - words made entirely from chemical element symbols Chemical element symbols can be combined to make English words. |

If you are typing a word, and your finger slips and hits one the the adjacent letters on the keyboard, what words could be made that are still valid? | |

Discrete Cosine Transforms - How JPGs work, and fun secret images Details about how JPEG compression works, how to move images from the spatial domain into the frequency domain, and how to combine images with different frequency components to make hybrid images. | |

How to share secrets securely (without breaking plates) How can you share a password amongst people so that a defined collection of them (but not all of them) is needed to recreate it? | |

Where should you stand to answer three phones? If you are standing next to a wall that has three phones that might ring at random, where should you stand to minimize the average distance you'd have to walk to answer phones if they ring? |

Analysis of emoticons used on Twitter What are the common emoji used in Twitter messages? | |

Prefixing 'S' to words to make new ones What words exist that you can add an 'S' to the front to make a new word? | |

Septic Feline - Twenty word puzzles answered by adding an 'S' A fun quiz in which the addition of a letter 'S' to the end of one word makes a totally different word. Crossword like clues are given. | |

Logic Puzzle - Gunman and colored dots A logic puzzle using red and blue dots on the forehead. | |

Rats live on no evil star - Palindromes and mirror words Words, that when written backwards, make new words. |

Is your password too predictable? An anlysis of the most popular PIN codes in use. | |

Which fits better - A round peg in a square hole, or a square peg in a round hole? Which makes a tighter fit? | |

Maximum Jeopardy! - What is the highest possible score in Jeopardy? If you answered every single question correctly, the board was configured just right, you uncovered the daily doubles at the appropriate time, and bet with confidence, how money is it possiblre to win on a single game of Jeopardy? |

A classic problem which requires you to place eight queens on a chess board so that no queen is attacking any other. | |

'Uncopyrightable' - Distinct letter words How many word exist in which every letter in the word is unique. | |

Parrondo's Paradox - Can two ugly parents make a beautiful child? Two games can be devised that, individually, lose money. However, paradoxically, If played alternately, can make money! | |

'I had no idea'. Ketchup, rockets, memes and pleated cups By relaxing the pleats of a sauce cup, it is possible to make it hold more ketchup. Just how much advantage does this provide? |

Wake up Redmond! (An open letter to Steve Balmer) Microsoft needs to quickly realize the world is moving mobile fast. | |

The two eggs interview question The classic interview question in which you need to determine the height an egg will not break when using the minimum number of drops, and just two eggs. | |

Intransitive Dice - How to use math to win free drinks from your friends! How to make a set of dice such that set A can beat set B, and set B can beat set C, but set C can beat set A. |

Minesweeper First Click: Quality vs. Quantity [GUEST POST] More advanced minesweeper techniques. | |

The Golden Gate Bridge is wider at the top than the bottom Consequences of living on a sphere. How far away in the horizon when you are sitting in a tree? How far apart are the tops of the Golden Gate bridge because of the curvature of the Earth? | |

Depending on how you lace your shoes, the answer could be different. | |

Where is the optimal location to click on classic minesweeper to maximize chances of opening a void? |

A collection of classic puzzle inspired by Martin Gardner. |

Space - It's mindbogglingly big! If you shrank the world down to the size of a tennis ball, how far away would the moon be? How about the sun? The next nearest star? | |

Hangman - You've probably been playing it wrong! There's no easy way to say this, but you've probably been playing hangman incorrectly your entire life. |

Benford's Law - Never try to defraud an engineer! Counterintuitive feature about real data and the frequency of occurrence of the first digit. | |

If you send sloppy morse code and the intra-letter and inter-letter gap become the same length what possible confusion can occur? | |

Padlock Puzzle - Databases and words Words formed that have the same displacement on letters along the word. | |

Analysis of registered domain names. | |

Steganography - How to secretly hide things The science of hiding information inside pictures so that it is not visible by the naked eye. |

State of the Union Address Analytics Analysis of the words spoken in Presidential State of the Union addresses. Which President did not say 'God'? Which President talked about 'War' most? | |

What is the probability of getting a Yahtzee? You have, up to, three rows. What is the probability of rolling a Yahtzee? | |

O! Say can you see … (Dating-mining the White House Visitor book) What can can we learning for examing the names of visitors to The White House? | |

Facebook finished 2011 with 791 million accounts Year end Monthly Active user count for Facebook, by year. | |

Where is the best place to aim on a dartboard to maximize the score you might achieve? |

Algorithm for playing Battleships What is the optimal strategy to employ when playing Battleship? | |

A photo tour of my visit to a Ukrainian undergroun missile silo. | |

Mathematical analysis of the game of Candyland® How long does a game of Candyland last? |

Mathematical analysis of the game of RISK® What is the best strategies to employ when playing Risk? | |

Markov Chains, Monte-Carlo and Chutes & Ladders! How long does a game of Chutes and Ladders last? |

Performance of one of the daily deal sites. | |

Latest WorldWide FaceBook registration statistics Wordwide Facebook stats for 2011. |

LivingSocial and the Whole Foods Coupon How quickly can you give away free money? |

Update on Worldwide facebook registrations per country Facebook stats in 2011 | |

Facebook stats in 2011 |

How Microsoft (used to) suck when it comes to treatment of thei guests. |

The amazing costs of various fluids when you normalize them as price per volume. | |

Facebook passes 666 million accounts Facebook stats. | |

Why has social gaming become so popular? The trifecta of reasons: Discoverability, Accessibility, Camaraderie. |

If you split a body up into elemental components, what would it be worth? |

Looking for Pi inside of Pi. |

Facebook was temporarily shut down in Egypt. |

Analyzing sales data using names (Part 3) Analyzing demographics of customers using just first names. | |

Data mining using just names. A study of names (Part 2) Androgynous names and death tables. | |

A rose by any other name. A study of names (Part 1) A study of the history of names. |

Generating sparks with recursion A mathematical way to generate spark effects. | |

Facebook stats for 2010 | |

What do all the people in this article have in common? | |

Do more men or women play social games? |

If you are going to travel, take one device. | |

Facebook Worldwide demographics (Part 2) Facebook stats. | |

Facebook Worldwide demographics (Part 1) Facebook stats. | |

How to proportionally break up a rectangular region. | |

Analysis of the relationship status of facebook users. | |

Digital Shakespeare (and data cleanliness) Which actors are on stage at the same time? | |

N-gram analysis on classic pieces of literature. |

A fascinicating day trip to the site of the horrible Chernobyl accident. |

My computer plays better Bejeweled than I do A cheap web cam and a bit of code. |

A 'practical' use for Genetic Programming Teaching my computer how to paint. |

Play better poker in just five minutes A poker strategy card product I designed a few years ago. |