Monday Maths Madness 15

As it is Hallowe'en this Wednesday, I have some Hallowe'en themed maths madness! Muahahaha

This is probably the only kind of pumpkin pie I like...

More pumpkin pi! Apparently there aren't a lot of Hallowe'en maths jokes on the internet. In fact I could only find one other. This one seems really popular out on the web.

Why do mathematicians sometimes confuse Halloween and Christmas?
Because Oct 31 = Dec 25.

Basically counting to 31 using base 8 is the same as counting to 25 using base 10 (and yes I did just have to write out all the numbers to check I was explaining the joke right...). It just so happens that October 31st and December 25th are significant dates in the calendar. Spooky!

Happy Hallowe'en everyone! :)

The Dominoes and the Chessboard

On Monday, I posted a puzzle regarding a chessboard and some dominoes. As promised, I am now going to give the answer (so that my boyfriend's family will stop arguing about it!)

So, is it possible to place 32 dominoes, each covering two squares, on a chessboard with two diagonally opposite corners cut out?

The answer is: No. It is not possible.

But how do you prove it? Most of the modules in my degree this term are all about proving things, and it can get very confusing. Especially Analysis. But there is a simple way to think about this puzzle.

As the two corners cut out of the chessboard are diagonally opposite each other, they must be the same colour. This means that we have 30 of one colour (in the picture above it is black) and 32 of the other colour (obviously, in this case white). As the dominoes only cover two squares, no matter how you place them, they are going to cover one of each colour. So if we pair off the colours, we can match 30 black to 30 white, but then we are left with 2 of the same colour left over. We know that a single domino cannot cover two squares of the same colour, so the puzzle is therefore impossible.

Hopefully I explained that clearly so you aren't left feeling as confused as before!

Monday Maths Madness 14

This week I have another puzzle for you to ponder over (just one this time, I promise!) I think I've heard of this puzzle before, but I read about it recently in Mathematics: A Very Short Introduction by Timothy Gowers and thought I would share.

The basic idea, is you have a chess board with two corners cut out like so:

 

You also have 31 dominoes that each cover two squares. Can you lie all of the dominoes on the chessboard, so they cover it completely?

Answer in a few days!

Edit: Ok, it's not totally obvious from the picture, but the top left and bottom right squares have been cut out.

Monday Maths Madness 13

Back to pictures this week. My boyfriend keeps sending me links to pictures on 9gag.com that are maths related, so I have enough to do a post about them!

This is a bit what I feel like in my lectures at the moment! Especially Analysis. You think it's simple, but when you actually come to write it down, there are no words to explain it.

The square root of a negative number is called an imaginary number. Anything else is a real number. Squaring an imaginary number makes it real. Shit just got real.

This is my personal favourite. I'm doing a lot about planes in Intro to Geometry at the moment. So far there have been no snakes though... Just triangles.

A nice surprise

I like getting maths book shaped presents :) Thank you Kirk!

Monday Maths Madness 12 (part 2)

As promised, here are the answers to the puzzles I gave on Monday.

1. Fumbling in the dark.

I would need to take 4 shoes to be sure of having a pair that match. If you took only 3 shoes, you could have taken one of each pair, so taking one more ensures you definitely have a pair of matching shoes.

Similarly, I would need to take 3 socks to be sure of having a pair that match.

2. Animal Farm

He would still have 50 horses - calling a cow a horse doesn't make it a horse.

3. Sum for simpletons

56 = 7 x 8

4. An up and down kind of existence

There is an absolute certainty that the monk will be at the same point on the road at the same time of day. Because the monk leaves later and arrives earlier on the second day than on the first day, there isn't a time of day on the second day that he was walking when he wouldn't have been on the first day. Therefore, if you imagine both journeys being made on the same day by two different monks, there comes a point where the two monks would have to walk past each other.

Monday Maths Madness 12

For anyone who is into Strictly Come Dancing, you will know that one of the celebrities is Johnny Ball. Johnny Ball is a TV personality from the 70s and 80s, and is known for popularising maths and science for children.

A little while ago, I can't remember exactly when, my mum bought me a book written by Johnny Ball. It is called Ball of Confusion, which is a collection of puzzles to do with maths, inspired by when he presented a puzzle on Zoe Ball's (his daughter) Radio 2 show. As Strictly just started this last weekend, I thought I would give a few puzzles from the book for you to ponder over.

1. Fumbling in the Dark

The lights have gone out - I said we should never trust wind farms - and I have to search my wardrobe in the dark for a pair of shoes and socks.

I have 3 pairs of shoes, 12 pairs of black and 12 pairs of brown socks.

How many of each do I need to take, to be sure I have a matching pair of each to wear?

2. Animal Farm

A farmer has 20 goats, 30 cows and 50 horses. How many horses would he have if you called the cows 'horses'?

3. Sum for simpletons

Look at this: 12 = 3 x 4.

Can you think of four other consecutive digits that do that?

4. An up and down kind of existence

A monk lives on a river bank in a valley. Once a week he must travel to the monastery at the top of the Lonely Mountain. He sets off at dawn, as the road is steep and long, and he arrives as the Sun sets. Next morning he has a lie in and leaves for home at 10am. As the road is downhill all the way, he arrives home at around 3pm.

What are the chances of the monk being at exactly the same point on the road, at exactly the same time on both days?

Answers on Wednesday! (Just to annoy my sister :P)

Monday Maths Madness 11

I have a few A Mathematician And... jokes for you this week.

A physicist and a mathematician are sitting in a faculty lounge. Suddenly, the coffee machine catches on fire. The physicist grabs a bucket and leap towards the sink, filled the bucket with water and puts out the fire. Second day, the same two sit in the same lounge. Again, the coffee machine catches on fire. This time, the mathematician stands up, got a bucket, hands the bucket to the physicist, thus reducing the problem to a previously solved one.

A biologist, a physicist and a mathematician were sitting in a street cafe watching the crowd. Across the street they saw a man and a woman entering a building. Ten minutes they reappeared together with a third person.
- They have multiplied, said the biologist.
- Oh no, an error in measurement, the physicist sighed.
- If exactly one person enters the building now, it will be empty again, the mathematician concluded.

Several scientists were all posed the following question: "What is 2 * 2 ?"
The engineer whips out his slide rule (so it's old) and shuffles it back and forth, and finally announces "3.99".
The physicist consults his technical references, sets up the problem on his computer, and announces "it lies between 3.98 and 4.02".
The mathematician cogitates for a while, then announces: "I don't know what the answer is, but I can tell you, an answer exists!".
Philosopher smiles: "But what do you mean by 2 * 2 ?"
Logician replies: "Please define 2 * 2 more precisely." 
The sociologist: "I don't know, but is was nice talking about it".
Behavioral Ecologist: "A polygamous mating system".
Medical Student : "4" All others looking astonished : "How did you know ??" Medical Student : :I memorized it." 

A physicist, a mathematician, and a mystic were asked to name the greatest invention of all time. The physicist chose the fire, which gave humanity the power over matter. The mathematician chose the alphabet, which gave humanity power over symbols. The mystic chose the thermos bottle.
"Why a thermos bottle?" the others asked.
"Because the thermos keeps hot liquids hot in winter and cold liquids cold in summer."
"Yes -- so what?"
"Think about it." said the mystic reverently. That little bottle -- how does it *know*?"

A mathematician, a physicist, and an engineer were traveling through Scotland when they saw a black sheep through the window of the train.
"Aha," says the engineer, "I see that Scottish sheep are black."
"Hmm," says the physicist, "You mean that some Scottish sheep are black."
"No," says the mathematician, "All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black!"

A mathematician, a physicist, and an engineer are all given identical rubber balls and told to find the volume. They are given anything they want to measure it, and have all the time they need. The mathematician pulls out a measuring tape and records the circumference. He then divides by two times pi to get the radius, cubes that, multiplies by pi again, and then multiplies by four-thirds and thereby calculates the volume. The physicist gets a bucket of water, places 1.00000 gallons of water in the bucket, drops in the ball, and measures the displacement to six significant figures. And the engineer? He writes down the serial number of the ball, and looks it up.

There are many more here. Enjoy!