July 2010
5 posts
My Weekly Top 5 Artists →
Sigur Rós (16)
Counting Crows (13)
Joshua Radin (6)
Jeff Buckley (2)
Blue Roses (1)
3 tags
Tuesday Teaser #20
It’s the Salem witch trials and two villagers are accused of being witches.
The witch-finder-in-chief says “There is a very simple test to tell whether you are witches. Each pick a card from a deck, and you can look at it if you want. But what I want you to do is predict the color of the other person’s card.
I’m going to put you in separate rooms so there is no communication between you. And if...
My Weekly Top 5 Artists →
Five for Fighting (12)
Blue Roses (10)
Death Cab for Cutie (9)
Explosions in the Sky (8)
Sufjan Stevens (7)
2 tags
Answer: Tuesday Teaser #19
The textbook answer to this is to name the North Pole as the only place where it can be done. Indeed, it is definitely true that the North Pole is the only place where you can walk a mile south (to a point A, say), then a mile east (to a point B, say) and then a mile north, arriving back where you started, such that point A is not equal to point B. However, what if point A is equal to point B?...
My Weekly Top 5 Artists →
Beach Fossils (19)
Wild Nothing (12)
The Gaslight Anthem (12)
Explosions in the Sky (11)
Jeff Buckley (10)
June 2010
9 posts
2 tags
Tuesday Teaser #19
This week’s puzzle is an absolute classic with a great (and perhaps surprising) solution:
How many points are there on Earth where you can walk one mile south, then one mile east, then one mile north and end in the place that you started? For the sake of argument, assume the Earth is a perfect sphere (of course).
My Weekly Top 5 Artists →
The Gaslight Anthem (41)
The National (14)
Jeff Buckley (12)
Jónsi & Alex (12)
Joseph Arthur (1)
2 tags
Answer: Tuesday Teaser #18
The trick to this puzzle is to look at the glass side-on and imagine it in two dimensions as a simple rectangle. Now, if you tip the glass so that the water touches the rim of the glass, the water will form a line that approximately meets the opposite diagonal. If the line meets the glass above the opposite diagonal, then the glass must be more than half full and vice-versa.
My Weekly Top 5 Artists →
Wild Nothing (64)
Frightened Rabbit (11)
Delorean (10)
The National (5)
Fleet Foxes (5)
4 tags
World Cup 2010 Preview
With less than 24 hours to go, I’m incredibly excited about this year’s World Cup. It looks to be one of the most open tournaments that I can remember, with plenty of genuine contenders for the title. There are nine countries who I think could realistically win the trophy (Argentina, Brazil, England, France, Germany, Italy, Netherlands, Portugal, Spain), but there are plenty of good...
2 tags
Tuesday Teaser #18
An easier and less mathematical riddle this week for the benefit of @aliholli and @nixenpixen:
Suppose you’re in an empty room with no method of escape. The only object in the room is a transparent glass of water. The glass is a perfect cylinder which looks half full, though you can’t be sure exactly. You are only allowed to leave the room if you can accurately determine whether the...
My Weekly Top 5 Artists →
Wild Nothing (24)
Beach Fossils (11)
Stornoway (8)
Brian Fallon of The Gaslight Anthem (8)
The Radio Dept. (5)
2 tags
Answer: Tuesday Teaser #17
Incredibly, they aren’t the same. Let’s calculate the two using conditional probability:
In the first problem, we want to find the probability that both children are boys given that at least one of them is. Using the formula for conditional probability this is equal to:
P(Both children are boys AND at least one child is a boy)/P(at least one child is a boy)
It’s clear that...
My Weekly Top 5 Artists →
Stornoway (56)
Beach Fossils (31)
Josh Ritter (22)
Laura Veirs (13)
The Radio Dept. (8)
May 2010
7 posts
3 tags
Tuesday Teaser #17
A brilliant, although completely useless, counter-intuitive probability puzzle this week.
If I have exactly two children and at least one of them is a boy, what is the probability that both of them are boys?
If I have exactly two children and at least one of them is a boy born on a Tuesday, what is the probability that both of them are boys?
Are these two probabilities the same or does the...
My Weekly Top 5 Artists →
The Radio Dept. (51)
The National (20)
Brian Fallon of The Gaslight Anthem (8)
The New Pornographers (6)
Laura Veirs (6)
2 tags
Answer: Tuesday Teaser #16
Tricky one to explain this one, you may need a pen and paper to cumulate the totals. So we start with two 8-litre jugs, let’s call them A and B, and an empty 3-litre jug, let’s call that C.
3 litres A => C => Pool 1
3 litres A => C
2 litres A => Pool 2
3 litres C => A
3 litres B => C => A
3 litres B => C
2 litres C => A
1 litre C => Pool 3
2...
My Weekly Top 5 Artists →
The National (33)
Laura Veirs (23)
MGMT (18)
Mumford & Sons (12)
Delorean (10)
My Weekly Top 5 Artists →
The New Pornographers (29)
Josh Ritter (26)
Joshua Radin (24)
Laura Veirs (19)
Langhorne Slim (12)
3 tags
Tuesday Teaser #16
A Die Hard with a Vengeance style puzzle this week, but significantly harder (sorry @aliholli)!
Suppose you have two 8-litre jugs full of water and an empty 3-litre jug. Your aim is to transfer exactly four litres of water into four separate pools. Assume that:
The only source of water is the 16 litres in the two 8-litre jugs;
Once water has been added to any of the pools, it cannot be...
2 tags
April 2010
6 posts
3 tags
Answer: Tuesday Teaser #15
Since we’re making two random cuts, let’s mark the first cut as x and the second cut as y.
It’s clear that we can’t always make a triangle, but what exactly are the conditions we need to have to make a triangle? Well, we simply need that for the longest side to be shorter than the sum of the two shorter sides.
In the case where x < y, we have the three sides x, y-x and...
My Weekly Top 5 Artists →
Laura Veirs (31)
Mumford & Sons (18)
The National (16)
Death Cab for Cutie (10)
Jónsi (9)
3 tags
Tuesday Teaser #15
Suppose I have a stick that is 1m long. If I break the stick in two random places (to form three pieces), what is the probability that I can form a triangle?
My Weekly Top 5 Artists →
Jónsi (77)
Jónsi & Alex (27)
Langhorne Slim (26)
Frightened Rabbit (20)
Fleet Foxes (16)
5 tags
Grand National 2010
I’ve never been a particularly big gambler (unlike aliholli who recently withdrew some winnings from her Betfair account to purchase a shiny new netbook*), but I’ve always had a tenner on the Grand National, Britain’s most valuable National Hunt race. This started in 2005 when, knowing nothing other than the fact that Ruby Walsh was “a bit good”, I staked £10 on...
2 tags
Answer: Tuesday Teaser #14
The first thing to note with this puzzle is that in order to minimize the number of planes required we want to keep as many planes as possible close to the island. For this reason, the best strategy is going to involve sending my plane around the far side of the world alone, so the question is how to get my plane to the 1/4 point with a full tank and how to fuel my plane back from an empty tank at...
March 2010
11 posts
2 tags
Tuesday Teaser #14
Imagine that I live on a small Indonesian island on the equator, where I own a fleet of 100 identical planes. It has been a life-long ambition of mine to fly along the equator all the way around the world. Assume the following rules:
Each plane has a fuel tank that, when at maximum capacity, can contain enough fuel to fly exactly half-way around the world.
All of the planes travel at the same...
My Weekly Top 5 Artists →
Jónsi (24)
Explosions in the Sky (18)
The National (9)
Mumford And Sons (8)
Joanna Newsom (7)
2 tags
Answer: Tuesday Teaser #13
The answer is yes. Here’s how:
If you choose to go first and place your first coin in the centre of the table, you create a symmetric playing surface (symmetric about the coin you placed in the centre). This means that wherever I can put down a coin on my go, the same space exists on the opposite side of the table when it comes to your go. So as long as you follow that strategy, there is no...
My Weekly Top 5 Artists →
Freelance Whales (84)
The National (15)
Sufjan Stevens (11)
The Mountain Goats (5)
Animal Collective (5)
2 tags
Tuesday Teaser #13
You and I are sitting at a round table with a huge pile of round two-penny coins. I challenge you to a game. The rules of the game are that we’ll each take it in turns to place a coin on the table. The coin must fully fit on the table without overlapping any of the other coins. The winner is the person who puts down the last coin (i.e. the first person to run out of space to be able to put a...
My Weekly Top 5 Artists →
Freelance Whales (32)
The Ruby Suns (18)
Doveman (16)
The National (10)
Joanna Newsom (8)
4 tags
Answer: Tuesday Teaser #12
It’s easy enough to solve this puzzle by working through all the combinations, but there’s a more elegant and adaptable solution using conditional probability. Let’s define the events:
A: I throw three numbers in strictly increasing order;
B: I throw three different numbers;
Then we can easily see the probability of B and the probability of A given B.
P(B) = 1 x 5/6 x 4/6...
My Weekly Top 5 Artists →
The Ruby Suns (51)
Wild Beasts (35)
Five for Fighting (11)
Bat for Lashes (5)
Fanfarlo (3)
3 tags
Tuesday Teaser #12
Back to dice probability for this week’s teaser:
If I throw three 6-sided dice one by one, what is the probability that I roll three numbers in strictly increasing order?
As an added bonus, enjoy OK Go’s incredible new video here.
My Weekly Top 5 Artists →
Fleet Foxes (33)
Sigur Rós (27)
The Pains of Being Pure at Heart (14)
Five for Fighting (12)
Explosions in the Sky (7)
February 2010
9 posts
My Weekly Top 5 Artists →
Freelance Whales (21)
Dan Auerbach (14)
Fanfarlo (11)
TV on the Radio (11)
Jónsi (9)
3 tags
Quick Sunday Trivia
A few London themed trivia questions for a Sunday evening:
What is the oldest London Underground line?
Can you name the thirteen bridges of Central London?
Fill in the missing blank in this famous quote about a street in London:
“You must not miss _________. At one end you will find a statue of one of our kings who was beheaded; at the other, a monument to the man who did it.That is...
My Weekly Top 5 Artists →
Fanfarlo (61)
Freelance Whales (23)
Blue Roses (11)
Doveman (10)
Dan Auerbach (8)
3 tags
Answer: Tuesday Teaser #11
There are many ways to answer the first three, but here are my favourite answers:
1. “I am not a knight.”
2. “I am a knave.”
3. “If someone asks me whether I’m a normal, I’ll answer ‘Yes’.”
Clearly if a knight or a knave were to say any of 1, 2 or 3, they would have to be lying or telling the truth respectively.
The second of the...
My Weekly Top 5 Artists →
Sufjan Stevens (30)
Freelance Whales (22)
Fleet Foxes (16)
R.E.M. (13)
Blue Roses (11)
1 tag
Quick Monday Trivia
Can you name the ten countries of the world whose names are only four letters long?
See the comments for the answer.
My Weekly Top 5 Artists →
Death Cab for Cutie (18)
Fleet Foxes (14)
R.E.M. (13)
The National (13)
Freelance Whales (13)
2 tags
Tuesday Teaser #11
Consider three types of people in a medieval kingdom - Knights, Knaves, and Normals. Knights always tell the truth, Knaves always lie, and Normals can do either. The King wants his daughter to marry a nice normal Normal, not one of those goody-goody Knights or devious scoundrel Knaves.
How can you make a true statement that will convince the King you are a Normal?
How can you make a false...
January 2010
8 posts
My Weekly Top 5 Artists →
Passion Pit (28)
Blue Roses (17)
Animal Collective (16)
Freelance Whales (11)
Explosions in the Sky (4)
3 tags
Catch-22
Over the last couple of weeks I’ve been reading Joseph Heller’s classic Catch-22, which I’m currently about halfway through. An FT quote on the back of the book reads: “Blessedly, monstrously, bloatedly, cynically funny, and fantastically unique.” I wasn’t sure what that meant until I started reading the book, but it’s now clear to me that the description...
2 tags
Answer: Tuesday Teaser #10
The answer is surprisingly simple. If at any stage somebody sits in your seat (number 50), then you will inevitably be forced to sit elsewhere. Similarly, if at any stage somebody sits in seat number 1, then each subsequent person will have their seat available and so you will end up sitting in your own seat. Now at each stage, while seats 1 and 50 are free, there is an equal chance of a person...