I have a board that uses the numbers 1 to 90. I fill the board with Othello piece, they are black on one side and white on the other. All the pieces start black side up. First I flip every second number, so 2 becomes white, and 4, 6, 8 and so on. Then I flip every third number, then every fourth number, until finally I flip every 90th number. Which numbers end up black side up and why?

Music by Ghostly Dust Machine http://freemusicarchive.org/music/Ghostly_Dust_Machine/Bad_Panda_79/Ode_To_A_Baby_Snowstorm

Maths Puzzle: Back to Black

A weekly homemade series of puzzles, tricks and mathematics from James Grime of Cambridge University.

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, and that the message will remain unbreakable, why is that? http://www.bbc.co.uk/news/uk-20456782

The curious case of the WWII carrier pigeon and the unbreakable code

A description of how I broke the code: http://www.singingbanana.com/codechallenge2012.htm

Here's another excellent explanation from Rule The Web (http://www.youtube.com/user/rtwvidz) http://ruletheweb.co.uk/blog/2012/03/singing-banana-code-challenge-2012/

QED Code Challenge 2012: solution and winners!

QED Gold: Originally uploaded 4th February 2011


Take a random pile of coins. If I tell you how many coins are heads and how many coins are tails, can you separate the pile into two piles with the same number of heads in each. And can you do this with your eyes shut?

Take the same number of coins as there are heads. Call this pile 1. Then;

Total number of coins in pile 1 = Total number of heads

In other words, if h1 and t1 are the number of heads and tails in pile 1, and h2 is the number of heads in pile 2, then;

h1 + t1 = h1 + h2

Cancel h1 on both sides and you will see that the number of tails in pile 1 will be the same as the number of heads in pile 2. So, if you turn over all coins in pile 1 you will now have the same number of heads in each pile.

Maths Puzzle: Coins Solution

QED Gold: Originally uploaded 31st January 2011.

Take a random pile of coins. If I tell you how many coins are heads and how many coins are tails, can you separate the pile into two piles with the same number of heads in each. And can you do this with your eyes shut?

Maths Puzzle: Coins

QED Gold: Originally uploaded 6th February 2011.

The Möbius Strip is a strange mathematical shape which is a loop with only one side and one edge. For more information see wikipedia: http://en.wikipedia.org/wiki/Mobius_strip

This is not a new idea, and for this and more mathematical valentines ideas see this blog: http://individual.utoronto.ca/sck/vday.html

Maths Puzzle: Back to Black

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