There are 100 ants on a board that is 1 meter long, each facing either left or right and walking at a pace of 1 meter per minute.
The board is so narrow that the ants cannot pass each other; when two ants walk into each other, they each instantly turn around and continue walking in the opposite direction. When an ant reaches the end of the board, it falls off the edge.
From the moment the ants start walking, what is the longest amount of time that could pass before all the ants have fallen off the plank? You can assume that each ant has infinitely small length.
The longest amount of time that could pass would be 1 minute.
If you were looking at the board from the side and could only see the silhouettes of the board and the ants, then when two ants walked into each other and turned around, it would look to you as if the ants had walked right by each other.
In fact, the effect of two ants walking into each other and then turning around is essentially the same as two ants walking past one another: we just have two ants at that point walking in opposite directions.
So we can treat the board as if the ants are walking past each other. In this case, the longest any ant can be on the board is 1 minute (since the board is 1 meter long and the ants walk at 1 meter per minute). Thus, after 1 minute, all the ants will be off the board.
You're standing in front of a room with one lightbulb inside of it. You cannot see if it is on or off. Outside the room, there are 3 switches in the off positions. You may turn the switches any way you want to. You stop turning the switches, enter the room and know which switch controls the lightbulb. How?
You turn 2 switches "on" and leave 1 switch "off" and wait about a minute. Then enter the room, but just before you enter, turn one switch from "on" to "off". Once in the room, feel the lightbulb - if it is warm, but off, it has to be the last switch you turned off. If it is on, it has to be the switch left on. If it is cold and is off, it has to be the switch you left in the off position.
Can you spot what's wrong with the following sentence?
PETER WAS ANGRY AT
HIMSELF BECAUSE HE
ACCIDENTALLY LEFT THE
THE KEYS TO HIS CAR
AT HIS FRIEND'S HOUSE.
Even though the odds are always in favor of the gambling house, why does the establishment insist on a house limit on stakes?
Every casino in the world would go bankrupt without a house limit on stakes. Without it, gamblers would keep doubling their stakes until they won. No matter how bad a losing streak they were on, they would eventually win. For more information, search: Martingale
Marty and Jill want to copy three 60 minute tapes. They have two tape recorders that will dub the tapes for them, so they can do two at a time. It takes 30 minutes for each side to complete; therefore in one hour two tapes will be done, and in another hour the third will be done. Jill says all three tapes can be made in 90 minutes. How?
Jill will rotate the three tapes. Let's call them tapes 1,2, and 3 with sides A and B. In the first 30 minutes they will tape 1A and 2A, in the second 3 minutes they will tape 1B and 3A (Tape 1 is now done). Finally, in the last 30 minutes, they will tape 2B and 3B.
