Challenge problems
Revision as of 18:08, 2 May 2015 by Ryan Moruzzi (talk | contribs)
| Problem 1 |
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| One hundred mathematicians are invited to the castle of Dr. Evil for an evil math convention. Before entering the ballroom, he gives each mathematician a hat with 7 accurate digits of pi on the front. No one sees their own hat but they are all told that at least one person has 7 accurate digits of pi on their hat. Next, Dr. Evil tells them to walk into the ballroom and stand in a circle so they can see every other mathematician. He tells them the lights in the ballroom will be continuously turned off then back on and as soon as you figure out if your hat as the accurate digits of pi on the front, you must leave the room when the light is turned off.
What is the minimum number of times the lights must be turned off so that everyone will have left the room? |
| Problem 2 |
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| Four cats are sitting at the four corners of a square. Each cat randomly picks a direction and starts to move along the edge of the square. What is the probability that none of the cats collide? |