Saturday, July 15, 2017

Circumnavigation


From 1519 until 1522, Ferdinand Magellan's Victoria was the first ship to successfully circumnavigate the globe. (Magellan himself did not survive the entire voyage.) Can you tell me which part of the ship traveled the greatest distance? Click below for the answer.




Replica of the Victoria, Photograph by Gnsin - Own work, CC BY-SA 3.0

Saturday, July 8, 2017

50 factorial


50! = 30414093201713378043612608166064768844377641568960512071337804000

Without doing the full computation, can you tell whether the above statement is true or false? Click below for the answer.


Saturday, July 1, 2017

The Missing Fish


Two fathers took their sons fishing. Each man and his son caught one fish, but when they all returned to camp they only had three fish. None of the fish were eaten, lost, or thrown back. How could this be? Click below to see the answer.




Saturday, June 24, 2017

Bags of Marbles


You have three identical bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white and one black marble. You pick a bag at random and draw out one marble. If the marble is white, what is the probability that the other marble in the same bag is also white? Click below to see the answer.




If you want to see how you would model this problem in Python, you can look at my solution on GitHub.

Saturday, June 17, 2017

The Monk and the Mountain Path


One morning at precisely 9:00 AM a monk begins walking up a mountain path. He takes his time, stopping several times to rest along the way. He arrives at the temple at the mountain's summit at precisely 5:00 PM that evening. The next day, the monk leaves the temple at precisely 9:00 AM and makes his way back down the path. Again, he takes his time and rests at several points along the journey. He arrives back at his original starting point at precisely 5:00 PM that evening. Is there any time when the monk is in exactly the same spot on both days? Click below to see the answer.





Saturday, June 10, 2017

The Pigeonhole Principle


The pigeonhole principle states that if a group of pigeons flies into a set of pigeonholes, and there are more pigeons than pigeonholes, then there must be at least one pigeonhole with two pigeons in it. More generally, if k + 1 or more objects are placed into k boxes, then there is at least one box containing two or more of the objects. Despite its seeming simplicity (perhaps obviousness), it can be used to solve a surprising range of problems in probability, number theory, and computer science, just to name a few. See if you can use it to solve the following three problems.

  1. (Warm up) A drawer contains a dozen blue socks and a dozen black socks, all unmatched. If the room is dark, how many socks do you have to take out to be sure you have a matching pair?
  2. Prove that there are at least two people in Tokyo with exactly the same number of hairs on their heads.
  3. Prove that if five distinct integers are selected from the numbers 1 through 8, there must be at least one pair with a sum equal to 9.

Click below to see the answers.




Saturday, June 3, 2017

Coffee with Cream


Suppose you have two cups in front of you, one with precisely 8 fluid ounces of coffee, and the other with precisely 8 fluid ounces of cream. You take precisely one teaspoon of the cream and add it to your coffee. You stir it in so that it's thoroughly mixed. Then you take precisely one teaspoon of that coffee/cream mixture and put it back into the cup of cream. Does the cup of coffee have more cream in it, or does the cup of cream contain more coffee? Click below for the answer.