Answer to the Good Will Hunting puzzle

In our Good Will Hunting podcast we asked:

What is the highest number of eggs that you CAN'T make, when you have boxes of size 6, 9 and 20?

Turns out this is called the McNuggest number as McNuggets originally came in boxes of this size.

In this case, it turns out that 43 is the largest number you can't make, but how do you prove it?

Well we note that:
44 = 4x6+20
45 = 5x9
46 = 6+2x20
47 = 3x9+20
48 = 8x6
49 = 9+2x20

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.


Simple, no?

Maths at the Movies: Fermat's Room

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.

Further reading links:

• videos of every puzzle from the film;
• a complete writeup of questions and answers from the film
• A duck popcorn maker, should you want such a thing.

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

Puzzle from Good Will Hunting

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.

Answer to A Beautiful Mind puzzle

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).

Maths at the Movies: Good Will Hunting

Last week we did A Beautiful Mind and now Good Will Hunting. We are really hitting all the well-known maths films at the moment aren't we?

More importantly joining us this week we have the wonderful

Dr James Grime

Philanthropist, playboy, billionaire... he is none of this things, but he may have identified the real Will Hunting!

This week we touch on such subjects as:

• Is University a scam?
• Good Will Hunting needs a prequel!
• Will James and Liz ever write a paper about the maths of Dirty Dancing?

 

If you're interested in watching Good Will Hunting you can follow the Amazon link below. 

Further reading links:

• What is the Hadwiger-Nelson problem and who is Aubrey de Grey?
• We also mention the fields of Combinatorics, Graph theory and Fourier theory.

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

Puzzle from A Beautiful Mind.

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?



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.