Author |
Topic: Lemming Drownings (Read 5107 times) |
|
william wu
wu::riddles Administrator
Gender: 
Posts: 1291
|
 |
Lemming Drownings
« on: Jan 22nd, 2003, 1:04pm » |
 Quote  Modify
|
Somewhere in Northern Eurasia, a group of 20 lemmings is planning a special group suicide this year. Each of the lemmings will be placed in a random position along a thin, 100 meter long plank of wood which is floating in the sea. Each lemming is equally likely to be facing either end of the plank. At time t=0, all the lemmings walk forward at a slow speed of 1 meter per minute. If a lemming bumps into another lemming, the two both reverse directions. If a lemming falls off the plank, he drowns. What is the longest time that must elapse till all the lemmings have drowned?
(if you make a certain cunning observation, this puzzle becomes trivial)
Note: Storyline inspired by the old video game Lemmings. Lemmings are mouse-like rodents rumored to commit group suicides, even though that's not really true -- a old Disney film inspired this myth. The video game Lemmings milks this myth. At the beginning of a level, hordes of the little creatures pour in a from the ceiling, and start walking forward foolishly, despite what perils may lay ahead (falling boulders, spiked pits, lakes of molten lava, etc.). The objective is to save them by building bridges, digging tunnels, and doing other ingenious manipulations of the environment.
|
| « Last Edit: Jan 22nd, 2003, 1:54pm by william wu » |
 IP Logged |
[ wu ] : http://wuriddles.com / http://forums.wuriddles.com
|
|
|
S. Owen
Full Member
Gender:
Posts: 221
|
|
Re: Lemming Drownings
« Reply #1 on: Jan 22nd, 2003, 2:30pm » |
Quote Modify
|
Very satisfying little puzzle, Mr. Wu. With a knowing wink, I will agree that I never could tell those darn lemmings apart either. Indeed.
|
|
IP Logged |
|
|
|
Speaker
Uberpuzzler
Gender:
Posts: 1118
|
|
Re: Lemming Drownings
« Reply #2 on: Jan 23rd, 2003, 12:26am » |
Quote Modify
|
Well, I want to clarify a few things.
What is the interval between lemmings?
I know this doesn't answer the question, but if you can fit ten 10cm long lemmings per meter, and all the lemmings were placed on the last two meters of the plank facing the end, then the shortest time would be two minutes as the little rodents trot right into the deep.
The longest time that might pass is quite a bit more difficult, and finding the answer is, I am chagrined to admit, not helped by S. Owen's hidden statement. 
|
|
IP Logged |
They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety. <Ben Franklin>
|
|
|
william wu
wu::riddles Administrator
Gender:
Posts: 1291
|
|
Re: Lemming Drownings
« Reply #3 on: Jan 23rd, 2003, 1:13am » |
Quote Modify
|
The lemmings are placed at random positions along the plank. I guess I'm implying equally random positions. So the interval between lemmings varies randomly. Treat the lemmings as dots with no thickness like in geometry, and the plank as a line.
Hehe. Some more hints:
Forgot about the storyline -- just picture dots moving on a line in the manner described in the riddle. Perhaps then it will be eaiser to see how S.Owen's statement applies.
|
|
IP Logged |
[ wu ] : http://wuriddles.com / http://forums.wuriddles.com
|
|
|
BNC
Uberpuzzler
Gender:
Posts: 1732
|
|
Re: Lemming Drownings
« Reply #4 on: Jan 23rd, 2003, 1:25am » |
Quote Modify
|
A-ha! Would the answer be 100 seconds?
My reasoning is this:
Say two lemmings, L1 and L2 walks toward each other. Say L1 walk in the +X direction, and L2 in the -X. Now they bump. L1 reverses direction to -X, and L2 to +X. So what? There is still one lemming going +x, and 1 lemming going -X. So, once one lemming starts walking toward the edge from distance D, one lemming will fall off (maybe a different one) after D/V (V being the velocity). So, longest time would be if a lemming was to be positioned at the very end of the plank.
|
| « Last Edit: Jan 23rd, 2003, 1:26am by BNC » |
IP Logged |
How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
|
|
|
william wu
wu::riddles Administrator
Gender:
Posts: 1291
|
|
Re: Lemming Drownings
« Reply #5 on: Jan 23rd, 2003, 2:29am » |
Quote Modify
|
Yes, congratulations  The velocity was defined as 1 meter per minute though, so the answer would be 100 minutes. Key observation is that (SPOILER) two lemmings bumping into each other is comparable to two lemmings passing each other.
|
| « Last Edit: Jan 23rd, 2003, 2:29am by william wu » |
IP Logged |
[ wu ] : http://wuriddles.com / http://forums.wuriddles.com
|
|
|
wowbagger
Uberpuzzler
 
Gender:
Posts: 727
|
|
Re: Lemming Drownings
« Reply #6 on: Jan 23rd, 2003, 2:31am » |
Quote Modify
|
I agree with your reasoning, BNC, but the correct answer is 100 minuts, right?
S.Owen:
That was really nifty wink.
|
|
IP Logged |
"You're a jerk, <your surname>!"
|
|
|
Speaker
Uberpuzzler
Gender:
Posts: 1118
|
|
Re: Lemming Drownings
« Reply #8 on: Jan 26th, 2003, 7:58pm » |
Quote Modify
|
Okay, I say 100 minutes too, which I figured out before peeking. That is I peeked at S.Owens comment, but not at the others. But, I have looked at them now.
I used the same reasoning, that if two lemmings are walking towards each other, then they will need to cover the same distance whether they rebound off each other or if they pass through each other.
Anyway, late, but not forgotten.
|
|
IP Logged |
They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety. <Ben Franklin>
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print