New PDF release: The Maths Notebook

By Tony Knight

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Sample text

Rather than look at the chances of the same birthday, let’s look at the chances of everyone having different birthdays. Again we assume that there are 366 days in the year. Person 1 This person can have any birthday. This doesn’t tell us anything. Person 2 This person can have any birthday except Person 1’s. We don’t know on which day Person 1 was born but there are 365 days out of 366 available on which Person 1 wasn’t born on. 73%. 56 Person 3 This person can have any birthday except Person 1 and Person 2’s.

In front of you are three doors. Behind one of them is a gold bar. Behind the other two are dustbins. You choose a door and keep whatever you find behind it. But there is a twist. Once you have chosen a door, I will open one of the remaining two and show you a dustbin, leaving two doors unopened. You then have the choice to stick with your original choice or swap doors”. What is the best strategy and what is your chance of winning the gold bar ? 59 The host knows where the gold bar is and, given that there are two dustbins, he can always show you one of them.

If the legend is true, at least we have some time to say goodbye to our loved ones ! The Tower of Hanoi puzzle was invented in 1883 by a French mathematician called Edouard Lucas. Lucas is best known for his results in number theory. His achievements include working out the formula for Fibonacci numbers and devising a clever way of testing primality (whether or not a number is a prime number or not). In 1876 he proved that 2127 - 1 is prime; this is the largest prime number ever discovered without the aid of a computer.

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The Maths Notebook by Tony Knight


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