March 2010
11 posts
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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...
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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...
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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...
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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...
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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.
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