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5 December
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This puzzle has five unrelated parts.
Show your work.
- You have bags A, B, and C, each containing two marbles.
Bag A contains two red marbles, Bag B contains two blue marbles, and Bag C contains one red marble and one blue marble.
You pick at random a bag and one marble out of that bag.
It is a red marble. What is the probability that the remaining marble from the same bag is also red?
- Hunter Jack wants to shoot a bear.
He leaves his camp, and walks 10 miles south where he perceives bear tracks.
Jack follows the bear tracks for 10 miles east, where he sees the bear and takes a shot at it.
Then Jack walks 10 miles north and is back at camp.
What is the color of the bear?
- Suppose we have a cube of cheese.
This cube is divided into 27 small cubes of cheese, so it looks like Rubik's cube (3 x 3 x 3).
There is this little mouse who wants to eat the whole cube of cheese.
She starts eating the cube in the center, and then has to continue eating adjacent cubes, where two cubes are called adjacent if they share a face.
Can the mouse eat the whole cube of cheese?
- At a restaurant, how could you choose one out of three desserts with equal probability with the help of just one fair coin?
- Both Al and Ben sell a basket of apples on the market.
They have the same number of apples, but Al's are Honey Crisps and Ben's are Braeburns.
So Al can sell his at 2 for 1 dollar, and Ben can sell his at 3 for 1 dollar.
Friend Chris walks by and is asked to sell the apples of Al and of Ben, who both have to go to a nearby bar to talk busines.
In their absence, Chris simplifies his job by mixing the apples of Al and Ben in one large basket, and sell
them at 5 for 2 dollars.
By the end of the day Chris is 1 dollar short.
How many apples did Al and Ben originally have?
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