Maths at: pi day

Happy pi day everyone. 

We figure that pi day is the like Hallowe'en for mathematicians. It's a day they get to cut loose and throw away their inhibitions.

As such Lorraine's intro pertaining to strong language is particularly pertinent for today's podcast. It starts out quite coarse.

So sit back, grab a slice of your favourite pie and enjoy as Ben sings you the song of his people.

Further reading links:

• Why not listen to our review of the film pi;
• The best web address known to man;
• The song from pi's digits;
• Search pi for meaningful numbers;
• Weird ways of calculating pi;
• Known digits of pi over time.

Subscribe via iTunes.

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

Puzzle from Interstellar

In our Interstellar podcast, Thomas posed the following puzzle:

A group of people with assorted eye colors (say 10 blue and 10 brown) live on an island.

No one knows the color of their eyes as there are no mirrors on the island and the water is muddy so you can't use the reflection. For all each person knows, they could have green eyes!

However, everyone can see the eye colour of everyone else, but they can't communicate to each other to tell each other their eye colour.

Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes can leave the island.

One day a sailor from the ferry gets off the boat and says:

"I can see someone who has blue eyes".

Everyone hears and understand the statement, but the sailor is immediately shot dead for communicating with the islanders and no-one ever speaks again. However, given this information some people are able to figure out their eye colour.

Who leaves the island, and on what night?

It's difficult, but possible.

If you think you have the answer comment below, tweet it to us @PodcastMathsAt, or email us at podcastmaths@gmail.com.

The answer will be posted next week.

Solution to The Oxford Murders puzzle

In our Oxford Murders podcast, Ben posed the following puzzle:

Suppose you are going to play chess against two people: one person is really good, one person is quite bad. You are going to play three games and you always have to alternate your opponents. Namely, you can either choose to play the opponents in the order

Good, Bad, Good,

or you can play the opponents in the order

Bad, Good, Bad.

Which of these two play sequences gives you the optimal chance of winning two consecutive games?

You can approach this problem using probability and tree diagrams. However a little logic goes a long way.

Specifically, in order to win two consecutive games you have to win the middle game. Thus, it is best to put your weaker opponent in the middle. Thus, Good, Bad, Good is the best strategy.

An alternative way of also seeing this answer it that you're probably going to lose against the good player, so the Good, Bad, Good play order gives you two chances to win against the good player, rather than just one.

Simple no?

If you want a bit more rigor then Ben has created a YouTube video solution.

Alternatively, you could try three player chess and team up with the weak player to beat the good player. But that might be considered cheating...

 

Puzzle from The Oxford Murders

In our Oxford Murders podcast, Ben posed the following puzzle:

Suppose you are going to play chess against two people: one person is really good, one person is quite bad. You are going to play three games and you always have to alternate your opponents. Namely, you can either choose to play the opponents in the order

Good, Bad, Good,

or you can play the opponents in the order

Bad, Good, Bad.

Which of these two play sequences gives you the optimal chance of winning two consecutive games?

If you think you have the answer comment below, tweet it to us @PodcastMathsAt, or email us at podcastmaths@gmail.com.

The answer will be posted next week, or you can listen to the answer in our Interstellar podcast

Flatland puzzle answer

In our Flatland podcast Thomas asked the question:

What is six divided by two plus one times two?

You can hear the solution in our Oxford Murders podcast or read on below.

So what did you get?

1?

4?
5?

Something else completely?

Well, whatever your answer is, you're completely correct (as long as you did the arithmetic correctly).

The problem with the phrase

What is six divided by two plus one times two?

is that it can be read in many different ways. For example, it could mean

6/2+1x2=5

or 

(6/(2+1))x2=4

or

6/((2+1)x2)=1

or

6/(2+1x2)=3/2

 The original statement is ambiguous and so providing a specific answer is difficult.

Your host, Thomas, was once interviewed on radio about a similar ambiguous statement. Have a listen below.

 

This sort of problem makes the rounds on the internet a lot, below is a Japanese version,

which shows that it is not just simply a problem with language. Mathematical operators can be written ambiguously as well.

Thus, if you arrive at such a question, the answer is not to angry, but try and understand how other people read the question.