At 6 a.m. a man starts hiking a path up a mountain. he walks at a variable pace, resting occasionally, but never actually reversing his direction. at 6 p.m. he reaches the top. he camps out overnight. the next morning he wakes up at 6 a.m. and starts his descent down the mountain. again he walks down the path at a variable pace, resting occassionally, but always going downhill. at 6 p.m. he reaches the bottom. what is the probability that at some time during the second day, he is in the exact same spot he was in on the first day?
You find an old treasure map in your grandma’s attic. the map shows a cannon, a coconut tree, and a palm tree. the map states that to find the treasure you must: a. start at the cannon, walk toward the palm tree while counting your paces. when you reach the palm tree, turn 90 degrees … Read More
A. first i would just like to say i am so glad jenna got voted off survivor. yuck, i couldn’t stand her ever since she accused that guy of eating beef jerky when he was chewing on grass. B. recruit meyer on boot camp rocks. did you see how he made himself cry to get … Read More
There are three ants on a triangle, one at each corner. at a given moment in time, they all set off for a different corner at random. what is the probability that they don’t collide? Solution Consider the triangle ABC. We assume that the ants move towards different corners along the edges of the triangle.
How many places are there on the earth that one could walk one mile south, then one mile east, then one mile north and end up in the same spot? to be precise, let’s assume the earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can … Read More
This is difficult to describe in words, so read this carefully, lest there be any confusion. You have a normal six sided cube. i give you six different colors that you can paint each side of the cube with (one color to each side). How many different cubes can you make?
I buried four fishermen up to their necks in the sand on the beach at low tide for keeping their fishing spot a secret from me. I put a hat on each of their heads and told them that one of them must shout out the correct color of their own hat or they will … Read More
You die and the devil says he’ll let you go to heaven if you beat him in a game. the devil sits you down at a round table. he gives himself and you a huge pile of quarters. He says “ok, we’ll take turns putting quarters down, no overlapping allowed, and the quarters must rest … Read More
There is a pot of N noodles. (so there are 2N ends). A person randomly grabs two ends and merges them. The person keeps doing it, until there are no more noodles, (and only loops), left in the pot. what’s the average number of loops in the pot?
A person dies, and arrives at the gate to heaven. there are three doors. one of them leads to heaven. another one leads to a 1-day stay at hell, and then back to the gate, and the other leads to a 2-day stay at hell, and then back to the gate. every time the person … Read More