##### July 2022

Perimeter Puzzle

What is the ratio between the perimeter of a circle to that of a square that touch as shown in the diagram?

##### May 2022

##### April 2022

##### January 2022

##### November 2021

##### October 2021

##### September 2021

52 card pickup

How many times will you need to pickup a randomly jumbled deck if each time you discard the face-up cards?

##### August 2021

##### July 2021

##### June 2021

Rolling, Banking, and Radioactive Decay

What is the expected number of rolls to bank three dice, if rolling a six banks any die, and how does this relate to radioactive decay?

##### May 2021

##### April 2021

##### March 2021

##### February 2021

##### January 2021

##### December 2020

Two Decks Puzzle

If you deal from two shuffled decks, in parallel, card by card, what is the probability that at least one pair of cards matches?

##### November 2020

Gender Identification Puzzle

How do you purchase a pair of chicks with the shortest number of trials?

##### October 2020

##### September 2020

##### August 2020

Red, White, Blue coin weighing puzzle revisited

Separating six coins in two weighings - a better solution.

##### July 2020

##### June 2020

Cut and Restored Checkerboard

If you cut, shuffle, and restore a 4x4 checkerboard, what are the chances you'll end up with a checkerboard again?

##### May 2020

50:50 Sock Puzzle

How many socks do you need to take to have a 50% chance of getting the pair you want?

##### April 2020

##### March 2020

Bucket of Dice

How many dice do you have to roll to have 95% confidence you'll get at least one six?

##### February 2020

##### January 2020

##### December 2019

The Best Full House

What is the best Full House you can be dealt in Poker? (Warning: You'll probably get it wrong)

##### November 2019

##### October 2019

Four Points Puzzle

How can you arrange four points so that there are only two distinct distances between any pair?

##### September 2019

Venture Beat Article

Thank you to my friend, Dean Takahashi, for writing a moving article about my condition.

Elf Chalkboard Puzzle

If math elves replace pairs of numbers with their differences, will the result be odd or even?

##### August 2019

Pearl Bracelet

What is the relationship between the diameter of a bracelet and the diameter of the pearls that make it?

##### July 2019

Approximating the Sine Function

How close can we get to approximating the trig function sine using very simple polynomials?

##### June 2019

##### April 2019

Word Ladder Solver (Longest Solutions)

Longest solutions to the distinct shortest lengths distinct word ladder problems.

##### March 2019

##### February 2019

Drones and Helicopters

Why are we trying to scale-up drones and not just use helicopters? It’s unmerited!

##### January 2019

##### December 2018

##### November 2018

Mirrors

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?

##### October 2018

##### September 2018

Overlapping Disks

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

##### August 2018

##### July 2018

Grazing and Calculus Revisited

Revisiting the optimal grazing field size using a barn and straight section fencing.

Poor Customer Service

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

##### June 2018

Lucy`s Secret Number puzzle

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

##### May 2018

Six Dice Betting Game

What are the chances that rolling six dice will result in four distinct numbers?

How digital cameras work

And the clever math that turns their color-blind sensors into full color images (plus some bonus calculus and interpolation).

How analog TV worked

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

##### March 2018

Turning Water into Wine

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

Sock Puzzle Revisited

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.

Nine digits puzzle

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

##### February 2018

Cribbage Scores

What is the distribution of all possible cribbage scores? (And what is the connection between Cribbage and nuclear submarines?)

Pancake Numbers

A classic problem involving the optimal way to flip a stack of pancakes into sorted order using just a spatula (prefix reversal). A young Bill Gates co-wrote a paper on this, and his upper bound solution was the best known solution for almost 30 years!

Superbowl Helmet Puzzle

A quick geometry puzzle for a shape that looks (a little) like a football helmet.

##### January 2018

Moravec's Paradox

Predicting the future is a crap shoot and, ironically, what appears to be hard is easy, and what appears easy, is really hard.

Shortest Crease Problem

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).

##### December 2017

##### November 2017

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.

##### October 2017

Multi Armed Bandit

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

##### August 2017

Poor Customer Support?

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!

##### June 2017

##### May 2017

##### April 2017

##### March 2017

Vestigial trigonometry functions

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

NSA Easter Egg Puzzle

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

##### February 2017

##### January 2017

Centroids of semicircles and hemispheres

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

##### December 2016

Mathematically, what is the optimal pitch for a roof?

Mathematically, what is the optimal pitch for a roof?

Think slow, think fast

Two simple math problems to which the first answer you give might not be correct.

##### November 2016

Grazing in a circular field

How long a rope do you need to allow a goat to graze half a circular field, if it is tethered to the circumference?

Aligned Clock Hands

How many times a day do the Hour, Minute, and Seconds hands of an analog watch align perfectly?

##### October 2016

##### September 2016

##### August 2016

Moscow Math Olympiad Puzzle

How can you and a friend publicly communicate about cards you are holding without a third person knowing?

Balanced Field Length

What is your best strategy if your plane experiences an engine failure during take-off?

##### July 2016

##### June 2016

##### May 2016

Blending independent estimates

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

Bisecting a triangular cake

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

##### April 2016

Baseball Card Collecting

On average, how many baseball cards do you need to buy to ensure you get a complete set?

##### March 2016

Two Bingo Ball Puzzle

If you draw two balls 1-75 and keep the highest one, what is the expected value?

##### February 2016

Two nugget problem

How do you determine the two heaviest nuggets (out of sixteen) in the least amount of weighings?

##### January 2016

##### December 2015

Estimating known unknowns

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

##### November 2015

##### October 2015

##### September 2015

##### August 2015

##### July 2015

Congruent Rectangles in a Square Puzzle

A geometry puzzle that, at first glance, appears to have not enough information to solve.

##### June 2015

Carnival of Mathematics

I will be hosting the August 2015 edition of the Carnival. Do you have any interesting facts about the number 125?

Standard Deviation Puzzle

What number can you add to the set {1,2,3} so that the standard deviation remains the same?

The Pardoner's Puzzle

Can you connect sixty-four towns with eight straight lines, and what is the connection with Harry Potter?

Five Circles Puzzle

Is it possible to draw five circles over a grid of 5x5 points so that at least one circle passes through every point?

##### May 2015

Clover Leaf Geometry Puzzle

What is the area of the shape described by the overlap of four inscribed semi-circles in a square?

Running Track Geometry

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

##### April 2015

Geometry Puzzle

What are the dimensions of an inscribed rectangle with the same area as an inscribed equilateral triangle?

Refuelling in cold weather

Can you save money by refuelling your car in the morning when the temperature is colder?

##### March 2015

Pi, PINs, and Permutations

How many digits of Pi do you need to ensure all possible 10,000 four digit PINs are included?

##### January 2015

##### December 2014

100 prisoner escape

A classic prison escape puzzle featuring 100 prisoners, 100 boxes and 100 tickets.

Dealer Button Bias

How much bias is there in selecting the position of the dealer by the first person to turn over an ace?

Impossible escape?

Can you use math to escape from, what seems like, an impossible prison escape problem based on coins and a chessboard?

##### November 2014

Giant iPad

If all the iPads in the World were combined into one giant device, what would it look like?

Triangular Trusses

What is the minimum number of crosses braces you need to make a rectangular grid stable?

##### October 2014

Red/Black Gambling Game

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?

Exciting soccer games and ballots

If you ultimately win a soccer game, what is the probability you were always winning?

##### September 2014

Optimal Rope Swing

Where should you let go of a rope swing to get the furthest distance into a lake?

Message in a bottle

Send and receive one-time anonymous fortune cookies to random people in the World.

##### August 2014

##### July 2014

Why are cans shaped the way they are?

What is special about cylinders, and why do they have specific aspect ratios?

Why are ice cream cones shaped the way they are?

Using calculus to optimize your ice cream consumption.

Carving Cylinders from Spheres

What is the largest volume cylinder it is possible to carve from a solid sphere? Also, so you know about the napkin ring problem?

Bad Hashing Function

Random trivia about converting words to numbers using the substitution cypher A=1, B=2 ...

##### June 2014

Coffee Time Challenges

Bite sized problems just hard enough to be tackled over a good cup of coffee.

##### May 2014

DataGenetics Greatest Hits

I've been writing my blog for three and a half years. Here are the top ten most read articles (per year).

Why do I blog?

I've been writing my blog for three and a half years. Why do I do it? How do I do it?

Amidakuji

Known as 'Amidakuji' or 'Ghost Leg' - The clever way that Asian nations randomly shuffle outcomes using just pen a paper.

Friday the 13th

The 13th of any month is more likely to fall on a Friday than any other day of the week!

##### April 2014

Holographic Replicators

What is the chance of escaping from a pack of angry, laser toting, monsters using a holographic replicator?

Geometric Mean

Calculating geometric means in SQL server without using aggregate functions, and why widescreen TV aspect ratio is 16:9

Minimum Jeopardy

What is the lowest, theoretical, score it is possible to score in a game of Jeopardy?

Fuel Consumption

Why we should really be quoting fuel consumption figures as 'gallons per mile' and not 'miles per gallon'.

##### March 2014

The Beauty in Mathematics

What is the connection between Moby Dick, accurate clocks, ski-jumps, roller coasters and cog wheels?

Marathon runners and WWII tanks

Estimating the number of runners in a marathon and spying on WWII German tank production.

Bounding Rectangles

The mathematics of repairing bullet holes in a wall using the smallest rectangle of drywall.

##### February 2014

The fallacy of The Gambler's Fallacy

I used to be superstitious, then I heard it was unlucky, so I stopped!

##### January 2014

Escaping from a monster in dark room

How do you escape from a monster in a dark room who has handcuffed you and given the key to a rat who runs off?

##### December 2013

Hiding from monsters using Corinthian columns

How to hide from a laser wielding monster (riding on a train) using a Corinthian column.

Mind Reading Magic Symbol Trick

Can your computer read your mind and predict the magic symbol you were thinking about?

Mind Reading Card Trick

Can your computer read your mind and make a card you were thinking about disappear?

Pixel Scalars

What algorithms do video game emulators utilize to scale up the low-res images, used on old computing devices, to modern hi-res standards?

Why do pipes burst the way they do?

Have you noticed that when pipes burst, they almost always burst the same way?

##### November 2013

##### October 2013

How to escape a monster (using calculus)

You are sitting in a rowing boat in the middle of a circular lake. How do you escape from a smart monster on the shore who can run four times faster than you can row?

##### September 2013

Privacy is dead! Long live Trust!

An honest discussion about what online privacy means in the 21st century.

Average Speeds

Is it quicker to walk backwards and forwards on a travelator or to simply walk there and back by the side?

##### August 2013

How to rotate an image

How to rotate an image, and a need trick to rotate a bitmap an arbitrary amount in a simple paint package.

##### July 2013

Exact Percentages and Prime Factors

Exact Percentages, Simplifying Fractions, Prime Factors and Greatest Common Divisors.

How much do you spend on coffee

Over a lifetime, with compound interest, it's probably more than you think!

##### June 2013

Selecting a random secretary

Selecting a random person (fairly) from an unknown number of applicants.

Sicherman Dice

Alternative ways to create dice that sum like a pair of regular dice (and how to cheat at craps!)

##### May 2013

##### April 2013

##### March 2013

##### February 2013

##### January 2013

##### December 2012

Random or Magic - Can you fool a computer at generating random numbers?

Flipping coins and making up numbers.

Trivial Wheel of Fortune bonus round

How lucky could you get? A list of English words you can make using only the letters: RSTLNE

##### November 2012

How to share secrets securely

How do you distribute a password amongst n-people so that not everyone needs to be present to recreate it?

##### October 2012

Ring, Ring! Where should you stand to answer three phones?

Where is the optimal location to stand to answer three phones to minimize the distance you need to travel?

Logic Puzzle - Gunman and colored dots

Can you use logic to save your life and determine the color of a dot painted on your forehead?

##### September 2012

Rats live on no evil star - Palindromes and mirror words

English words that make different words in reverse.

Round Pegs and Square Holes

Which is a better fit? A round peg in a square hole, or a square peg in a round hole?

##### August 2012

The eight Queens problem

How to place eight queens on a chess board so that no queen is attacking any other.

`Uncopyrightable` - Distinct letter words

Words that don't contain more than one instance of the same letter.

`I had no idea`. Ketchup, rockets, memes and pleated cups

How to maximize the amount of condiment in your cup.

##### July 2012

##### June 2012

Minesweeper First Click: Quality vs. Quantity

Guest Post - Further analysis on Minesweeper Clicking.

Consequences of living on a sphere

The Golden Gate Bridge is wider at the top than the bottom because of the curviture of the Earth.

How long are your shoelaces?

A brief look into the various methods that shoes can be laced and their relative lengths.

Advanced Minesweeper

Where is the best location to click when playing Minesweeper to maximize the chances of a cascade?

##### May 2012

##### April 2012

##### March 2012

Hangman - You've probably been playing it all wrong!

Learn the optimal strategy for playing Hangman.

Benford's Law - Never try to defraud an engineer!

The totally counterintuitive way that the leading digit of natural variables changes.

Analysis of Domain Names

Everything you wanted to know about domain names, and probably things you did not!

Steganography - How to secretly hide messages

Method for secretly hiding covert images inside other images.

##### January 2012

Analysis of State of the Union Address speeches

Deep dive into the words used in the last 82 Presidential State of the Union Addresses.

##### December 2011

##### November 2011

##### September 2011

##### August 2011

##### June 2011

##### May 2011

##### April 2011

##### March 2011

##### January 2011

Analysing sales data using just names

Part three of detailed analysis of names and how to use them to analyse sales data (links to preceeding two articles are in the document).

##### December 2010

##### November 2010

##### October 2010

##### July 2009

##### April 2009

##### January 2009

Play better poker in just five minutes

Strategy cards to teach you the relative odds of the starting cards.