What could be special enough to bring us back? Well nothing more than a bloomin' election! That's right we're going to look at how maths infuses even our democratic duties.
Today's discussion points:
How are Thomas and Liz now that they're parents?
How do we deal with having no perfect voting systems?
Rude diagrams and asymptotes.
All this and more in this week's Maths at.
In you're interested in more political theory then the UK will be going to the polls on November 12th! Enough stats to make you go blind.
Further reading:
This YouTube Playlist provides a really wonderful overview of why all voting systems are bad.
Take a look at what your vote is really worth at voterpower.org.
Marriages, prenancies, black holes, none of these stopped us getting the best quality maths film chat from our mouths to your ears. The question is: after all that will there be a third series?
Today's discussion points:
Are opinion polls pointless?
Which way does the inequality point?
What instrument can you play?
All this and more in this weeks Maths at.
In you're interested in watching Travelling
Salesman you don't need to buy it off Amazon, you can just watch it on
YouTube! Look a James Stewart's pretty face below.
Further reading:
Have a look at the New York Times' scathing review of this charming film.
The government didn't want you to hear this podcast. They tried to pay us off! Just remember as you listen to it: we are not responsible for any repercussions if you decide to watch Travelling Salesman.
Today's discussion points:
How many tickets do you have to buy to win the lottery?
Squashed research!
How many actors can you have playing the same character?
All this and more in this weeks Maths at
In you're interested in watching Travelling Salesman you don't need to buy it off Amazon, you can just watch it on YouTube! They can't even give it away!
Further reading:
Should you feel guilty about watching the film on YouTube, you can give the creators your money, through their official website.
Consider a clock with an hour hand and a minute hand. Starting from midnight, how many times do the hands cross each other in 24 hours.
Note, you don't count the starting point of midnight, with the hands overlapping as a crossing, but you do count the last moment, when the two hands overlap at midnight a day later.
Bonus Question:
Normally, clock hands travel clockwise around the clockface. Suppose now that the two hands are travelling in opposite directions. How many times do the hands cross in this case?
Well, this was a pain in the backside to edit. The film is so tawdry and dull that we kept getting lost on tangents. Fear not though faithful listener, Thomas has edited the two hours of guff down to a single hour of solid... bronze.
Today's discussion points include:
How should you flip a mattress?
Does the culture you grow up in influence how you learn maths?
BUMFIT!
From our mouths to your ears, enjoy!
If you want to watch x+y, you can follow the link below.
Further reading links:
As per usual some artistic license was taken with this true story, this website provides the fact behind the fiction;
one person randomly decides whether
to tell the truth or lie (assume lies and truth are equally likely);
the three know amongst themselves who they are.
You can ask two questions to the people. The answer to which
must either be yes or no. What question do you ask and who do you ask?
This is an extension of the famous two person puzzle. Normally, you only have two guards, one tells the truth and one lies. You have to choose and open one of the doors, but you can only ask a single question to one of the guards.
What do you ask so you can pick the door to freedom?
In this case the solution is: If I asked what door would lead to freedom, what door would the other guard point to?
This works by considering the two possible outcomes. Namely:
If you asked the truth-guard, the truth-guard would tell you that the liar-guard would point to the door that leads to death.
If you asked the liar-guard, the liar-guard would tell you that the truth-guard would point to the door that leads to death.
Therefore, no matter who you ask, the guards tell you which door leads to death, and therefore you can pick the other door.
The inclusion of the trickster guard, however, changes the puzzle dramatically. Specifically, you questions have to work no matter who is being asked (truth-teller, liar, or trickster). Further, no matter what you ask, you always
have to worry about the trickster screwing up your logic.
Thus, one strategy is to identify one person is NOT the trickster. We
don't have to identify whether they are truth-teller, or liar.
Call the three gaurds A, B and C. You ask A:
"Is exactly one of these statements true:
You are the truth-teller
B is the trickster
If you get back the answer yes, then the possibilities are:
A is the truth-teller and B is the liar (1. true, 2. false, so one statement true, so answer is yes which truth-teller truthfully gives)
A is the trickster
A is the liar and B is the truth-teller (both statements false so answer is no which liar lies about)
In all three cases, B is not the trickster.
If you get back the answer no, then the possibilities are:
A is the truth-teller and B is the trickster (both statements true, so answer is no which truth-teller truthfully gives)
A is the trickster
A is the liar and B is the trickster (1. false, 2. true so one statement true so answer is yes which liar lies about)
In all three cases, C is not the trickster.
Once you have found a person who is not the trickster, just point to a door and ask the person:
"Would your exact opposite say this door leads to freedom?"
If you're interested in the future of literature then have a look at Lyle's recent book. It discusses such subjects as: indie publishers, hybrid authors, and fanfiction writers.
Lyle's also written plenty of digital fiction. Again, this is reading, but not as we know it.
If you're lazy and got be bothered to read then why not try Lyle's podcast Wonderbox publishing.
one person randomly decides whether
to tell the truth or lie (assume lies and truth are equally likely);
the three know amongst themselves who they are.
You can ask two questions to the people. The answer to which must either be yes or no. What question do you ask and who do you ask?
Some further rules for the more pedantic:
You cannot ask questions like "Will it rain tomorrow?", because neither the truth teller, nor the liar can be sure.
You cannot ask questions like "What would you answer if I ask you
blablabla?", because if you ask the random liar they don't what their next answer will be.
You cannot ask something like "Will you answer No to this question?", because the truth-teller can't answer this question.
All decisions must be based on the yes and/or no answers only.
This puzzle is not about "how to find a way around the rules".
Since we have 6 consecutive numbers that can all be made from 6, 9 and 20, then every number there after can be made simply by adding an appropriate multiple of 6, e.g. 50 = 44+6, 51 = 45+6, etc.
Welcome to the strangely erotic episode of Maths at, where we watch the tense, psychological thriller, Fermat's Room (or La Habitación de Fermat, for you Spanish speakers) and we ask the real questions of... WHAT HAPPENED ON THE BOAT?
As per usual, the time line is all wonky. This episode does follow on from A Beautiful Mind, but was recorded a long time after, so although we talk about our lives having changed dramatically, it's only bee two weeks for you and you already know what's happened if you've listened to our Christmas episode. It's so hard living in a linear timeline.
So if you want to know:
what Liz's ovaries sound like;
which superpower our hosts would rather have;
how Ben would overhaul examination procedures,
then join us in our latest episode of being distracted by pop corn makers.
If you're interested in watching Fermat's Room and want an easier time than we had in finding it, simply click the Amazon link below.
Ben's local shop stocks eggs in boxes of capacity 6, 9, or 20 eggs. What is the highest number of eggs that you CAN'T make?
For example, you can make 29 with one 9 box and one 20 box, 29=9+20,
you can make 30 with a five 6 boxes, 30=5x6.
but you can't make 31.
For those wanting an extra puzzle, can you prove that your answer is correct. Namely, all numbers higher than your chosen integer can be written as a linear combination of 6, 9 or 12.
In our podcast episode on A Beautiful Mind
the following question was asked:
Two trains are on the same track. They start 100km apart and head towards each other at a speed of 50km/h.
Whilst
these two trains are heading for their collision a fly starts out on
the front of one train and zooms directly to the front of the other at a
speed of 75km/h (see the animation above). Once the fly reaches the
second train it immediately darts back to the front of the first train
at the same speed and repeats this back and forth motion until the two
trains collide and the fly is squashed on impact.
How far has the fly traveled, before it meets its demise?
One way to approach this problem is through infinite series. Namely, we find how far the fly during the first journey, the second journey, the third journey, etc. and add them all up. Thankfully, there is a fairly nice formula that provides this answer.
However, a much simpler way to calculate the distance is by realising that the changes in direction do not matter. Namely, all we are asking is how far can a fly travel in the hour it takes for the trains to hit each other? Clearly, this is simply 75 km. Sometimes, a moment's thought can save an hour's work!
As mentioned last time, John von Neumann was said to have immediately answered this problem, but when pressed on his solution method he said that he has used the infinite series method. Ah to have the mind of a genius!
This and other aspects of von Neumann's genius are discussed in Raymond Flood's excellent Gresham College talk, below (plus you get a bit of Alan Turing for free, which Thomas is always happy about).
A classic puzzle to start our second series. It appears in the background of A Beautiful Mind and it is said that the famous mathematician John von Neumann immediately answered with the correct result. But we'll talk about solutions later!
Animation illustrating the problem courtesy of MathWorld.
Two trains are on the same track. They start 100km apart and head towards each other at a speed of 50km/h.
Whilst these two trains are heading for their collision a fly starts out on the front of one train and zooms directly to the front of the other at a speed of 75km/h (see the animation above). Once the fly reaches the second train it immediately darts back to the front of the first train at the same speed and repeats this back and forth motion until the two trains collide and the fly is squashed on impact.
How far has the fly traveled, before it meets its demise?
The Christmas episode reveals secrets from later on in the series.
We tried to hide these secrets in the Mean Girls episode, which was recorded around seventh, but released first.
When we I say that we've had a complaint about Liz's language it from the pi day episode, not the Mean Girls episode.
Is that all clear? And this is all because the recording quality of this episode is a little dodgy!
Sorry about all that. Just pretend that Thomas, Ben and Liz are Time Lords.
Anyway, we had to get there eventually. Probably number one of many science film lists: A Beautiful Mind. The biopic of John Nash, a prodigy behind the field of game theory.
To help us discern our cooperators from our defectors we are joined by the wonderful
