Paradoxial games

This was a free lecture to anyone in Greenwich or out. The Greenwich MathSoc set this up with help from @NoelAnn and @Tony_Mann. When I was doing my last year at Greenwich Eduardo Cuntin did a project on paradoxical games giving the history off it and interviewing the man himself. So a couple of months later MathSoc asks him to come and then we have an event. A couple of people on twitter and facebook spread the word of the event. Then we are brought to the day of the event.

WARNING: if you are going to attend a lecture by Juan M.R. Parrondo do not read any further, if your interested in the maths contine.

The man who everyone came to see is Juan M.R. Parrondo was introduced by Noel-Ann Bradshaw and Eduardo Cuntin. This problem is apparently 10 years old. The idea is there is 2 games which if played individually will end up with you losing money (gambling is easier to visualise) but if you alternate between the 2 games randomly then you will win. Confused? read on.
He gave an example, Game A is a simple game you win with probability p1 and lose with p2. The second game Game B is more complicated if your capital is divisible by 3 then you win with prob p3 and lose with p4, if your capital is not divisible by 3 then you win with prob p5 and lose with p6. This should help visualise it

This is what happens when you play the games randomly or the games separate

As you can see playing randomly turns to be profitable (The above was the game being played 5000 times).

Apparently the trick to working out this paradox comes from something called Brownian motor and the probability of each game.

Game A has a small positive gradient and Game B is a mixture of 2 gradients 1 big positive gradient and one shallow negative gradient. Switching between the 2 games means you increase your profits. This website may explain the Brownian motor better.

There was some criticism of the paradox in 2004. They questioned the paper and said if it was not random but they got to pick which game they chose then their odds and profit would go up. This is true but if you deal with more than one person choosing between which game to play i.e. democracy then you will end up losing but random still triumphs.

The lecture ended.
Parrondo's paradoxical games homepage

Recreational Mathematics

At Greenwich today the maths society (MathSoc) arranged a lecture on the subject of "Recreational Mathematics" which was given by David Singmaster. Unfortunately after my first picture my iPhone lost internet connection. Here is my first pic:

If you did read his wiki article, you would know he is famous for his Rubik cube solution, so I was glad when he brought that out:

Unfortunately my memory sucks so I can only recoil memories from the pictures. So somehow we managed to get to a bit about labyrinths and he found one underground, this was him getting into the cave:

And the he presented the cave itself and a drawing of the labyrinth

We then moved on to the Fibonacci series and there was a weird pattern in there:

Its a bit hard to see but if you look at the 15th line where it begins 14,1,....., 1001, 2002, 3003.... Huh this is weird but wait, because of this the 16th line reads 15, 1,.....,3003,5005..... and again on the 17th line we get 16,1,...., 8008,..... Strange phenomenon, its uncommon and doesn't happen often.

He then showed us fibonacci work (I believe) and the numbers we now use today which he got when he travelled abroad.

We then looked at another bit of Fibonacci's work, which included work that showed how to use the numbers for adding and multiplying. No picture here as it seemed a bit boring.

Now we looked at problems and teapots. I'll get to the teapots in a minute. One problem we looked at was:

If you can't read it, it says

"As I was going to St. Ives, I met a man with seven wives, each wife had seven sacks, each sack had seven cats, each cat had seven kits. Kits, cats, sacks and wives. How many were going to St. Ives?"

The answer wonderfully is none. Or one if you count the man himself.
There was other puzzles but I forgot them and forgot to take a picture of the puzzles. Shame apparently those puzzles perplexed even the greatest mathematicians.

Okay now the teapot. David Singmaster brought one with him:

As you may notice although the picture isn't that good, it has no lid to speak of, so how do you use it I hear you ask. Well glad you did, because I wondered as well and here's how:

You fill it up from the bottom and then flip it over, wonderful.

Next we had a problem:

"Can you draw three rabbits with three ears between them and that each rabbit looks like they have two ears each"

Easy enough draw them in a triangle formation like so:

This is all well and good but this image has been used in loads of different places:

Then the lecture finished:

for the next hour or so any people who were left got to play around with some stuff he brought along i.e. teapot, rubik cube (3*3*3), rubik cuke (7*7*7), Rubik cube (1*3*3), bolts that were together, sheet of paper that looked like it had space in side of it and some more things I can't remember.
Actually one thing i did remember was a magic trick (apparently it actually something to do with physics) which was cool here is the 10 sec video:
Wordpress wants me to upgrade to put video on here so hello Twit Vid

This should be back dated to 10th of November 2010