Tuesday, 17 October 2017

Watch along with MATM

Coming this Friday Maths at: The Movies reviews The Man Who Knew Infinity, the biopic of the incredible genius of Srinivasa Ramanujan.

As you will not doubt have noticed, maths films bring in the acting powerhouses: Kevin Spacey, Gwyneth Paltrow,... Donald Duck!

This film is no different. Between Dev Patel's puppy dog eyes and Jeremy Irons' introversion this film has some interesting, sad and poignant moments.

Why not watch along with us? You can buy a digital version of the film by clicking on the image below.

Monday, 16 October 2017

Answer to "Seven Gold Rings"

In our "Proof" podcast, we set the following puzzle:

Tom employs a labourer, who is going to work for him for seven days.

Every day the labourer wants to be paid one gold ring for each day they have worked. So at the end of the week they should leave with seven gold rings.

Tom has a chain with seven gold links, but cannot simply give the laborourer all seven links, because the labourer wouldn't return. Equally, the labourer wants to ensure that they leave every day with as many gold links as days that they've worked, otherwise, they, again, won't return.
Tom could cut each link and pay the labourer one link per day, using seven cuts. But this wastes a lot of gold.

What is the minimum number of links that Tom must cut in order to make sure the labourer can always leave with the correct number of gold links?

What was your answer?
We can do it in one cut! Here's how:

Cut only the fifth ring.
and rearrange to form the binary sequence 1, 2 and 4 links.
Using these links we can pay the labourer the exact amount everyday, on the understanding that we can take back the links we've already given them.

Explicitly,
Day 1: give the 1 link piece;
Day 2: take back the 1 link piece, and give the 2 link piece;
Day 3: give the 1 link piece (the labourer already has the two, so they have three links altogether);
Day 4: take back the 1 and 2 link pieces and give the 4 link piece;
Day 5: give the 1 link piece;
Day 6: take back the 1 link piece, and give the 2 link piece;
Day 7: give the 1 link piece.

Thus, at the end of the seven days the labourer has all seven links and was never short-changed!

This puzzle relies on the fact that all the numbers between 1 and 7 can be written in binary, using three bits:
1=001,
2=010,
3=011,
4=100,
5=101,
6=110,
7=111.

Consider the extension to this problem. Tom wants the labourer to work for 15 days and has a chain of 15 gold links. What is the minimum number of cuts would he need to do now?

Think you know the answer? Comment below, tweet at us or email us at podcastmaths@gmail.com


Friday, 13 October 2017

Friday factoid- Friday 13th occurs far too frequently.

Friday 13th is an unlucky day in the UK. British people stay at home, don't make eye contact in public, and spend their day complaining, mostly about the weather.
Did you know, however, that the 13th is more likely to be a Friday than any other day? And also, coincidentally, Friday the 13th is the equally-most likely day number/day name combination to occur?

Why? We know the year for the Earth (the time it takes us to do one orbit of the Sun) is 365.242189 days. This is annoying for calendar makers, as we just can't put an extra 0.256 days into each year. So what do we do? Well, we try and even it out over a 400 year cycle. We fix the year to have 365 days normally (remember the old rubbish rhyme: "30 days has September, April, June and November, all the rest have 31, except February...")

February has 28 days, except in a leap year, where it has 29. A leap year is defined as
  • any year which is divisible by 4 except
  • years divisible by 100 are not leap years except
  • years divisible by 400 are leap years.
If we repeat this on a 400 year cycle, then this means that the average year length is 365.2425 days (or very close to it)
If we work out the number of days in 400 years, then this is 146097 days; by chance this is divisible by 7, so it means that if a day is a Monday, the same day 400 years later will be a Monday. In other words, the minimum period the calendar cycles over is 400 years. Note that 146097/400=365.2425, very close to Earth's year.

We can then run a simple computer script to count the number of times that each number/day of week combination occurs in a 400 year cycle, and graph the results

This shows us that the 13th is a Friday 688 days out of every 400 year cycle, more than any other day. Also, we can see that Friday 13th is the joint most common number/day of week combination (all the yellow squares in the diagram). I have left off the 29th,30th and 31st just because it's a nicer pattern this way.

So is this important? No! But next time you have bad luck on Friday 13th remember, this day will happen 688 days in the next 400 years so you'd better get used to it...


Friday, 6 October 2017

Maths at the Movies: Donald Duck in Mathmagic Land

In this episode we watch the movie Donald Duck in Mathmagic Land.

Well, this was just weird.

Although the animation is beautiful, can you trust the company that told you that lemmings were suicidal to teach you mathematics?

Also we cover Donald Duck's terrible gun control and the billiards game that goes on forever!

Plus bees that make jam.

If you're interested in watching Donald Duck in Mathmagic Land, you can follow the Amazon link below.

Further reading links:
Subscribe via iTunes.

Wednesday, 4 October 2017

So, how old is Ben?

If you remember, at the end of Maths at: the Movies, 21, we asked you how old is Ben on his next Birthday, if he is currently 50 years, 50 Months, 50 Weeks, 50 Days, and 50 Hours old?

The best way to answer this question is to start with the hours and convert them to days,
i.e. 50 hours = 2 days 2 hours.

Then convert the 52 days into weeks,
52 days = 7 weeks 3 days,
and so on.

Following this process you should discover that Ben is currently 55 years old and, thus, will be 56 on his next birthday.
Doesn't Ben look good for his age?
Of course the easiest way is to get a computer to do it. Wolfram alpha may not be good for much, but unit conversions are where it excels.

Not too difficult to start us off with, but did you get it right? Tweet at us, @podcastmaths, or find us on facebook, to receive a shout-out on a future podcast and a warm fuzzy glow.

Monday, 2 October 2017

Next up - Maths with Donald Duck!

There can be few more celebrated, more acclaimed, more accomplished mathematicians than Donald Duck.

For our next podcast "Maths at: The Movies" we're going to Mathmagic land with everybody's favourite Disney duck.... and you can watch this for free on YouTube.



Our podcast will be out later in the week, but tell us what you think in the comments below!

Quack quack!

Tuesday, 26 September 2017

Puzzle from Proof: Seven Gold Rings


In our latest podcast about the movie "Proof", we set the following puzzle:

Tom employs a labourer, who is going to work for him for seven days.

Every day he wants to pay the labourer one gold ring for each day they have worked.



Unfortunately Tom is a strange person who keeps his gold in the form of a chain with seven gold links, and a miser who doesn't like wasting gold. What is the minimum number of links that Tom must cut in order to make sure the labourer can always leave with the correct number of gold links?

Post your comments or answers below, and we'll give you the answer at the end of our next podcast.



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