Ants riddle

[EngIntoHW]

Hey,

I'd like to get your help with an additional riddle please

Here is goes:

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.


I know the answer, but I don't manage to prove it.
I'd appreciate your help

 

[Nameless1]

....urgh, i cheated and got the answer...but the solution I found made sense haha. Won't post it yet ;-)

 

[MrAl]

Hello,


Are we allowed to burn any with a magnifying glass?

 

[tvtech]

Hello,

Are we allowed to burn any with a magnifying glass?

LOL

That's really cheating.

Question: How do you Nuke an Ant??
Answer: With a magnifying glass and lots of patience. It will eventually catch fire. Albeit an extremely small fire though

This is funny. My imagination knows no bounds. Sorry guys but this is a hoot. Hope this thread lives forever.

Cheers

 

[dougy83]

Um, my small mind wonders what the difference in the result with the following 2 rules:

1) original: 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
2) alternate: The board is sufficiently wide that the ants can pass each other without incurring any delay.

In each case, the result of two ants meeting from opposite directions at point X results in two ants leaving point X in opposite directions. So it would seem to me that the longest time would be that of an ant travelling the full board length, which would be 1 minute.

 

[Ratchit]

EngIntoHW,

The smallest time is zero if you set the ants at the ends of the board and facing away from the center. In no time at all, they walk off the board.

The longest time is one minute if you set the ants at the ends of the board facing the center. It doesn't matter what the count is or how you distribute the ants, both groups will take one minute to drop off the board. When the two groups collide in the center of the board, the group members will change as described below. This is analogous to conservation of momentum for identical masses such elastic pool balls traveling at the same speed.

Take the case of two pool balls traveling in opposite directions and colliding. We initially have 1>--<2 before and after <1--2> . We still have 2 groups of 1 ball each going in the same direction, but the membership changed. Now consider an asymmetric group like the following coming together 1,2,3 >--<4,5 . Afterwards it will be <1,2--3,4 5> . After the collision, we will still have a group of three balls going from left to right and a group of 2 balls going from right to left according to the conservation of momentum. But again the membership of the group changed.

That shows that some of the ants will end up at the opposite end of the board and drop off and others will reverse at the center of the board and drop off at where they started. In both cases it will take one minute for each ant to drop, and they all will drop at the same time.

Ratch