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.
