## Morris: World Of Britain

I am in a total immersion game called ‘World of Britain’.

Every day you can take a daily task, if you dare.  There are five tasks and each day one of these tasks is given at random.  You could get the same task each day if you were unlucky.

·         Cycling in Edinburgh; the best city in the world has plenty of cycle lanes to help you avoid the traffic, some of them are a bit surprising.

·         Bog Snorkelling in Wales; my favourite British sport, bar none!  Watch the action here!

·         Gurning goes back to at least the thirteenth century.  You may think it is just about pulling funny faces, and you would be right.

·         Mud Racing  How do you know who won?

My math question is:  assuming you win everything you enter how many days would you expect it to take to win all of these competitions?

p.s Gurning is now international.  Here is a US gurner completely oblivious to the exciting belly-flop championship happening behind him.  Apparently “everyone and their butt crack is welcome”

## Morris: The Kate Bush Conjecture

Thanks to my second favourite math radio programme, More or Less, for this wonderful new insight into music and maths.

In her song, Pi, Kate Bush sings the first one-hundred and fifty or so digits of the celebrity number.

This is what she sang:

3.14159265358979323846264338327950288419716939937510582319749

44592307816406286208 8214808651328230664709384460955058223

You don’t need me to point out the wrong digits do you?  Good.  Then we can move on.

This has led to the Kate Bush Conjecture.  Since Pi contains an infinite sequence of digits which never repeat surely the sequence Kate sings must occur somewhere!  She never says she is starting at the beginning.

The Weak Kate Bush Conjecture says:

The sequence Kate sings exists somewhere in the decimal expansion of Pi.

The Strong Kate Bush Conjecture says:

Kate could have sung any finite sequence of digits and it would exist somewhere in the decimal expansion of Pi.

If Pi were a random sequence of digits then both conjectures are true.  But Pi isn’t random, it is a well-defined number so we can’t make any assumptions.  Instinctively I think it must be true, but that isn’t good mathematics, we need to prove it!

For example the following number is infinite and non-repeating but it doesn’t satisfy either conjecture:  0.01001100011100001111…

If the strong conjecture is true then every finite sequence exists in Pi.  And they each exist an inifinite number of times since they can occur in an infinite number of longer sequences.  Think about that, an infinite number of sequences each occurs an infinite number of times.

Everything that can be encoded digitally would occur within Pi.  That would include the complete works of Shakespeare, naturally, and also the note you left for the milkman last Tuesday, and those poems you wrote when you were five.

Every religious book, all cannons and all translations, both forwards and backwards.  Every prayer, every satanic chant and every children’s song.

That picture of the cosmic microwave background, the observations of Tycho Brahe and all of Kepler’s notes; and the results from CERN that will prove the Higgs-Boson (come on guys!)

It would include everything on your iPod, every episode of Math Factor and an alternative Math Factor with Groucho Marx.

Every album by Bob Dylan, or Kate Bush.  And everything you’ve sung in the shower.

It would include this post and all the comments you will make, or think about making.

It would include every thought and idea you have ever had, or ever will have, or ever could have.  (Gödel may have something to say about that)

And you thought Kate Bush was just a singer.

And you thought Pi was just a number.

## Morris: Turning Tables

I took one of Peter Winkler’s puzzle books on holiday recently.  After dinner each night I intended to impress my friend with an amazing math puzzle.  I had done this before.

The book dissapeared on the flight out.  After dinner each night my friend impressed me with an amazing math puzzle.  I haven’t seen the book since.

Serves me right!

This is one of those puzzles, you will understand why I have to do it from memory.

I really like Jeff’s post  A Fun Trick – Guess the Polynomial.  You might want to look at it first.

If you relax the conditions a bit you have a similar sounding puzzle with a very different solution.

So my puzzle is this:

I am thinking of a polynomial.  All of the co-efficients are fractions.   You may use any number as your test number.  When you give me a test number I will tell you the result.

How many test numbers do you need to identify the polynomial?

## Morris: How to Win Your Bonus

Sometimes rules set up to achieve one result can have exactly the opposite result.

## Morris: Inside Every Hexagram …

Inside every hexagram there is a cube trying to get out but, just like the thin woman hiding inside Eddie, it isn’t that easy to spot.

New Scientist magazine has a regular math puzzle called Enigma.  A few years ago they posed this intriguing problem.

‘Assign the numbers 1 to 12 to the twelve vertices of a hexagram so that the sum along each line is the same.’

At first sight this is the worst possible kind of puzzle.  You have to try lots of ways of assigning numbers until you stumble across the right answer.  Very boring!

The best kind of puzzle is when you spot a neat insight that makes everything easy.

Guess what, that is exactly what we are going to do here!

## Morris: Christmas = Halloween?!?

For me the holidays end on Monday so I just have time to post this seasonal question.

Why is Christmas the same as Halloween?

Specifically why is Oct. 31 = Dec. 25.

Hint: you need to look at exactly how this is written.

A short problem with a long pedigree.

I found this in Martin Gardner’s book ‘The Colossal Book of Short Puzzles and Problems’, problem 3.9 in my copy.  He credits Solomon Wolf Golomb, the inventor of Polyominoes which inspired tetris.

Isaac Asimov based a whole story on this puzzle,  ‘A Curious Case of Income Tax Fraud’, part of his Black Widowers series.

Enjoy!

Steve

## Morris: Sequences and Scrabble

Happy New Year Math Factor fans.

My name is Stephen Morris and like Edmund I’m going to be posting in the Math Factor website.  I have been a listener for some time and have posted comments as ‘stevestyle’.  I’m not a professional mathematician, just a keen amateur and fan of math puzzles.  I live in England.

I thought I would start with an anecdote from the recent holidays, where playing scrabble with the family helped with one of Chaim’s problems.  I hope you enjoy it.