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Matching socks

Isn’t it annoying when trying to pair up a pile of socks, just how many single socks build up before you finally start finding matches for them?

So, how many single socks might we expect to have at various times in our pairing exercise?

We need first to ask this question in a more precise manner. There are two related but separate versions of this question.

But before we start, some ground rules…

Just don’t get me started on odd socks – finding the planet where they go is another much more complicated problem, which I’ll leave to astrobiologists and ufologists. So, here we’re thinking only about sock piles with no odd socks. 

We will also ignore our natural ability to easily see the two bright orange socks in the pile and pick them out as a pair straight away. That is, we assume each sock is chosen from the pile completely at random, then checked to see if it matches any other previously selected single sock.

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What’s the smallest number not found on Google?

A simple question really, if potentially self-contradictory.

Any 10 digit number I tried seemed to be a phone number – are there any which are not?

Even some 11 digit numbers suffer (in this context) the same fate. (This has changed quite a bit since 2008 – see here.) But, after 20 minutes searching, I did find… wait! If I write it down here as is, then, when Google indexes this page, it will cease to be not on Google.

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Factor Dates and Times

We’re coming up to 4 April 2016, or 4/4/16.  Notice that, on this day, the day of the month multiplied by the number of the month equals the two digit year i.e.

4 x 4 = 16

That was also the case on 8 February 2016, and will be again on 2 August 2016.  How often do this or similar events happen?

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Friday the 13th

Do you suffer from paraskevidekatriaphobia (the fear of Friday 13th)? Well may you do so, for the 13th day of a month is (slightly) more likely to be a Friday than any other day of the week. And 2015 has had three Friday the 13ths (the most possible), so it’s no wonder you’re ducking for cover at the slightest hint of trouble.

How might this happen? Surely things average out in the end? Well, no.

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Harry Potter time turning

I confess that I’m an information junkie. I’m also fascinated by the myriad different ways of presenting information.

About a year ago, the excellent XKCD site had a post with movie narrative charts. They show the power of graphical display to convey information in a way not possible with words. Visual representation of film character groupings can be understood much more naturally. Symbols are used for particular event or action types.

These charts, particularly for The Lord Of The Rings, inspired me to try a similar thing for the ‘time turner’ part of Harry Potter and the Prisoner of Azkaban.

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Birthdays – Get in line

Imagine a line of people, one behind the other, all facing the same way (to the head of the line).

You get a prize if you are the the first person in the line (from the front person,  working backwards) to have a person ahead of them with the same birthday.

Where to stand to have the best chance of getting the prize?

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Mazes of every shape

Some years ago, I wrote a program which could make mazes of arbitrary shapes. Some of the most popular shapes are that of names. For example, using my daughter’s name and a weave pattern she thought of:


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