# singingbanana

• ### Wythoff's Game (Get Home) - Duration: 4 minutes, 52 seconds.

• 3 months ago
• 80,064 views
Wythoff's Game is played on a chessboard. Two players take it in turns to move a piece. That piece can move any number of square to the left, and number of squares down, or any number of squares on...
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• ### Game: Get Home - Duration: 3 minutes, 57 seconds.

• 3 months ago
• 74,907 views
A game with a winning strategy.

Place a piece a grid (like a chessboard). Two players take it in turns to move the piece. You can move any number of squares to the left; and number of squares down...
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• ### Twin Primes Problem - Duration: 65 seconds.

• 6 months ago
• 62,756 views
Prove that when you multiply a pair of twin primes you get a number that has remainder 8 after division by 9. With one exception.

I'm already getting some good solutions. It's interesting to see p...
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• ### Cambridge has a new mathsy train station - Duration: 2 minutes, 59 seconds.

• 6 months ago
• 127,476 views
Cambridge North is the new train station in Cambridge which features a mathematical design. The architects said the design was "derived from John Conway's Game of Life". Except it's not the Game of...
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• ### A visit from Rafael Procopio (Matemática Rio) - Duration: 87 seconds.

• 1 year ago
• 23,967 views
I was visited by Rafael Procopio from Matemática Rio.

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• ### Origami Soma Cube - Duration: 2 minutes, 22 seconds.

• 1 year ago
• 66,998 views
The soma cube is a famous puzzle among mathematicians. Seven tetris-like pieces fit together to make a 3x3 cube. I made one from post-it notes.

My instructions for the sonobe units: https://www.yo...
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• ### Sum of Fibonacci Numbers Trick - Duration: 6 minutes, 8 seconds.

• 1 year ago
• 219,818 views
A little trick to sum Fibonacci numbers. Try it out.
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• ### The International Maths Salute with Dr James Tanton - Duration: 91 seconds.

• 1 year ago
• 32,330 views
I caught James at the MATRIX conference in Leeds in September 2016. I'm a fan of his work so this was cool. We grabbed a moment to make a super quick video.

Go see James' videos on his YouTube cha...
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• ### Ten years on YouTube - Duration: 47 seconds.

• 1 year ago
• 37,960 views
Jim Bob scores a hat trick https://youtu.be/HkcoKbr5NjQ
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• ### Ramanujan Review - Duration: 117 seconds.

• 1 year ago
• 49,914 views
A sort of review of The Man Who Knew Infinity. And a *review* of other videos that came out this week.

standupmaths: Ramanujan, 1729, Fermat's Last Theorem https://www.youtube.com/watch?v=_o0cIpLQ...
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• ### Ramanujan Summation - Duration: 8 minutes, 46 seconds.

• 1 year ago
• 151,571 views
The third video in a series about Ramanujan.This one is about Ramanujan Summation.

Euler-Maclaurin...
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• ### Ramanujan's Pi Formula - Duration: 4 minutes, 21 seconds.

• 1 year ago
• 253,873 views
The second video in a series about Ramanujan. Continuing the biography and a look at another of Ramanujan's formulas. This one involves Ramanujan's pi formula.
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• ### Ramanujan: Knowing The Man Who Knew Infinity - Duration: 4 minutes, 39 seconds.

• 1 year ago
• 100,130 views
The first video in a series about Ramanujan. A bit of biography then a look at one of Ramanujan's formulas. This one involves infinite nested radicals.

Here's a more formal look at Ramanujan's nes...
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• ### Married Problem survey result - Duration: 90 seconds.

• 1 year ago
• 49,709 views
Here is my solution video: https://youtu.be/pTpBcxIg-9A

Here is the solution and results from the problem by Alex Bellos https://www.theguardian.com/science/2016/mar/28/did-you-s......
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• ### Married Problem with solution (plus extra problem) - Duration: 9 minutes, 17 seconds.

• 1 year ago
• 169,433 views
Jack is looking Anne, but Anne is looking at George.
Jack is married, but George is not.
Is a married person looking at an unmarried person?
A) Yes B) No C) Cannot be determined

Here is the soluti...
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• ### Married Problem - Will 80% of people get this problem wrong? - Duration: 89 seconds.

• 1 year ago
• 70,049 views
Jack is looking Anne, but Anne is looking at George.
Jack is married, but George is not.
Is a married person looking at an unmarried person?
A) Yes B) No C) Cannot be determined

Unfortunately the ...
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• ### Maths Puzzle: The self descriptive number solution - Duration: 13 minutes.

• 1 year ago
• 157,566 views
Solution to the self descriptive number puzzle https://www.youtube.com/watch?v=K6Qc4oK_HqY

Here is the original version of the proof presented in the video http://singingbanana.com/self%20describi...
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• ### Maths Puzzle: The self descriptive number - Duration: 77 seconds.

• 1 year ago
• 78,159 views
I have a ten digit number. The first digit tells me how many zeros are in the number. The second digit tells me how many ones are in the number. The third digit tells me how many twos are in the nu...
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• ### 2016 - The start of a new (dozenal) century - Duration: 4 minutes, 39 seconds.

• 1 year ago
• 94,230 views
2016 is the beginning of a new century - if you count in twelves. If you do that then the year 2016 becomes the year 1200.

Counting in twelves is known as the dozenal system, and a "century" in d...
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• ### Cheryl's Birthday Problem - It depends on your point of view - Duration: 9 minutes, 7 seconds.

• 2 years ago
• 172,297 views
Cheryl's Birthday problem was a question in a recent Singapore Maths Olympiad. Here is the problem:

You have Albert, Bernard and Cheryl. Cheryl says "my birthday is one of these ten dates"

May 1...
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• ### The Imitation Game Reaction - Duration: 6 minutes, 34 seconds.

• 3 years ago
• 77,773 views
For more of my thoughts read The Imitation Game FAQs here http://aperiodical.com/2014/11/an-alan-turing-expert-answ...
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• ### Lorenz: Hitler's "Unbreakable" Cipher Machine - Duration: 11 minutes.

• 3 years ago
• 107,647 views
Many people have heard of Enigma before, the code machine used by Nazi Germany to send secret coded messages. Yet, some very clever code breakers were able to break that code and read those message...
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• ### Cubic Curve Calculator - Duration: 5 minutes, 58 seconds.

• 3 years ago
• 83,911 views
Turn a cubic curve (with no x^2 term) into a calculator for sums, multiplications and square-roots.

Simply draw a line across the curve so that it intersects at three points, a, b and c. We may no...
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• 2048 strategy and maths from Steve's channel

### 2048 strategy and maths - Duration: 24 minutes.

• 3 years ago
• 446,580 views

You can play 2048 here:
http://gabrielecirulli.github.io/2048/

You can watch it being played by AI here:
http://ov3y.gi...
• ### 2048 Induction Extra - Duration: 8 minutes, 51 seconds.

• 3 years ago
• 65,410 views
An extra bit from our 2048 video on Steve Mould's channel.

Full video here: 2048 strategy and maths http://youtu.be/OO4tA5i7X9g

Play 2048 here http://gabrielecirulli.github.io/2048/

------------...
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• ### Building Houses Solution - Duration: 7 minutes, 2 seconds.

• 3 years ago
• 62,719 views

Imagine the line from 0 to 1. Write a sequence of points such that the first two points occupy different halves, the first three occupy dif...
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• ### Building Houses Problem - Duration: 3 minutes, 23 seconds.

• 3 years ago
• 69,543 views
Imagine the line from 0 to 1. Write a sequence of points such that the first two points occupy different halves, the first three occupy different thirds, the first four occupy different fourths, an...
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• ### New Wikipedia sized proof explained with a puzzle - Duration: 10 minutes.

• 3 years ago
• 588,399 views
A new mathematical proof was in the news this week, which partially solves the Erdos Discrepancy Problem. The proof was described as "bigger than Wikipedia". I attempt to explain the problem using ...
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• ### There are always two opposite points on the Earth with the same temperature - Duration: 2 minutes, 12 seconds.

• 3 years ago
• 247,740 views
There are always two points on opposite sides of the Earth with the exact same temperature. And we can prove that.

Temperature changes continuously. If a and b are on opposite sides of the equator...
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• ### The Riemann Hypothesis - Duration: 19 minutes.

• 3 years ago
• 412,605 views
The Riemann Hypothesis is one of the Millennium Prize Problems and has something to do with primes. What's that all about? Rather than another hand-wavy explanation, I've tried to put in some detai...
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• Milking this material one more time:

### The Maths of Star Trek - Duration: 25 minutes.

• 4 years ago
• 118,737 views
The science of Star Trek has, in the past, been discussed in great detail - but what about the maths of Star Trek?

Star Trek: The Original Series contains a surprising amount of mathematics, inclu...
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• ### Maths Problem: Complete Noughts and Crosses (Burnside's Lemma) - Duration: 7 minutes, 39 seconds.

• 4 years ago
• 152,570 views
How many ways are there to complete a noughts and crosses board - an excuse to show you a little bit of Group Theory. Rotations, reflections and orbits - oh my!

Burnside's Lemma http://en.wikipedi...
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• ### Maths Problem: Complete Noughts and Crosses (tic-tac-toe) - Duration: 119 seconds.

• 4 years ago
• 79,506 views
How many ways are there to completely fill a Noughts and Crosses (tic-tac-toe) board, with four noughts and five crosses? Not including rotations and reflections.

Question sent to me by http://www...
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• ### Grime Dice Juggling Balls - woo! - Duration: 2 minutes, 53 seconds.

• 4 years ago
• 34,369 views
Grime Dice juggling balls made for me by Pat Ashforth from http://www.woollythoughts.com/grimedice.html

For more information, see my video and article on Grime Dice http://grime.s3-website-eu-west...
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• ### More Maths Trolling - Duration: 5 minutes, 17 seconds.

• 4 years ago
• 156,123 views
Riemann Series Theorem may be used to show ln(2) = (1/2)*ln(2)

A formula for natural log: ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + ... for |x| less than or equal to 1.

So ln(2) = 1 - 1/2 + 1/3 - 1/4...
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• ### MinutePhysics Maths Trolling (Adding Past Infinity) - Duration: 5 minutes, 43 seconds.

• 4 years ago
• 375,090 views

Unlike convergent series, divergent series do not have limits (the sum of the first n ter...
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• ### See my response to 'How Predictable Are You' on the IMAmaths channel - Duration: 31 seconds.

• 4 years ago
• 44,357 views
I've made a response to Richard Wiseman's video 'How Predictable Are You' from his Quirkology Channel. The video is not here but featured on IMAmaths - the YouTube channel for the Institute of Math...
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• ### The Catenary - Mathematics All Around Us. - Duration: 4 minutes, 14 seconds.

• 5 years ago
• 96,813 views
The catenary is the natural shape of a free hanging rope or chain and can be found everywhere. From the the wires of a pylon to the thread of a spider's web. From the world of bubbles to the world ...
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• ### The curious case of the WWII carrier pigeon and the unbreakable code - Duration: 6 minutes, 16 seconds.

• 5 years ago
• 42,167 views
A British couple discover the remains of a WWII carrier pigeon behind their chimney. It was carrying a coded message. Code experts believe the code used was something called a One-Time Pad Cipher, ...
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• ### Another Lock Puzzle - Duration: 63 seconds.

• 5 years ago
• 44,539 views
Imagine a combination lock with three wheels. The wheels are labelled with the numbers 1, 2, 3. Turn the wheels and numbers increase, until 3 turns back to 1. You may only turn the first two wheels...
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• ### de Bruijn Card Trick - Duration: 4 minutes, 23 seconds.

• 5 years ago
• 53,881 views
Before christmas I showed you some sequences called de Bruijn sequences. They're designed to contain every combination of some numbers without any repeats http://youtu.be/iPLQgXUiU14

For example, ...
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• ### Another Lock Puzzle Solution - Duration: 2 minutes, 38 seconds.

• 5 years ago
• 43,109 views
Solution to the puzzle http://youtu.be/23U0X4moMCI
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• ### Final video of Turing Week - Duration: 68 seconds.

• 5 years ago
• 9,263 views
Three Turing videos:

Alan Turing - Celebrating the life of a genius: http://youtu.be/gtRLmL70TH0
Alan Turing and Animal Patterns: http://youtu.be/TLfRbJ_3r3g
Campaign for the Turing Tenner: http:/...
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• ### Alan Turing and Animal Patterns (morphogenesis) - Duration: 8 minutes, 19 seconds.

• 5 years ago
• 21,081 views
James Grime and Thomas Woolley in conversation about Alan Turing, morphogenesis and animal patterns.

Turing's original paper: The chemical basis of morphogenesis http://www.dna.caltech.edu/courses...
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