Dinosaurs
On the island of Triassic, the Dinosaur population, thought to be near extinction, has expanded enormously. We know now two facts about them:
1> There are 400 Dinosaurs
2> No Dinosaur has more than 50 wrinkles on his body
From this we can deduce that there must be two Dinosaurs with the same number of wrinkles?
1> There are 400 Dinosaurs
2> No Dinosaur has more than 50 wrinkles on his body
From this we can deduce that there must be two Dinosaurs with the same number of wrinkles?
Labels: logic
posted by Rajesh Lal at
6:01 PM
17 Comments:
If wrinkles were evenly distributed, then there would be 400/50 = 8 dinosuars with each number, 1 thru 50. If they were unevenly spaced there would be some wrinkled sets with more than eight, but there MUST be at least two dinosuar with duplicate numbers of wrinkles.
I dunno mathematically but logically there have to be atleast 2 dinosaurs with the same number of wrinkles (most probably more).
Lets take an example of 50 rooms and 400 people. If all 400 are to be put in the 50 rooms, there has to be atleast 1 room with more than 2 people. In some rooms there might be more than 2 also because the ppl wont be evenly distrbuted.
This is assuming that the quizzer has made a gramatical mistake in the last line.
"From this ""we can"" deduce that there must be two Dinosaurs with the same number of wrinkles?"
I am assuming that it is:
"From this ""can we"" deduce that there must be two Dinosaurs with the same number of wrinkles?"
I like the anology given by AJK.
This is true, it would be like
400 people divided into 50 rooms.
It would be possible to to assign the first 50 to fifty different rooms, but then when you got to the 51 person you would then have to begin doubling up.
Dinosaurs are extinct...
" Ragknot said...
If wrinkles were evenly distributed, then there would be 400/50 = 8 dinosuars with each number, 1 thru 50. If they were unevenly spaced there would be some wrinkled sets with more than eight, but there MUST be at least two dinosuar with duplicate numbers of wrinkles. " Couldn't it be possible that there are two dinosaurs with 200 wrinkles? Wouldn't that be even distribution too?
If all but one dinosaur have NO wrinkles then no two dinosaurs have the same number of wrinkles - but only if you assume that zero is NOT a number.
Looks like http://en.wikipedia.org/wiki/Pigeonhole_principle also known as Dirichlet's principle
I dont really understand why the last sentence was a question.....
well... if you are thinking with all the math then yes. but since dinosaurs like humans are always different form one another than no.
seeing as this is a trick question the answer is most likely very simple. So I'm guessing that the answer is no, because at this point there are no dinosaurs therefore the have no skin to measure the wrinkle. But idk.
No dinosaurs. No wrinkles. Have we gone back years...
hello, im ashley and im 15. i got really bored at home and i downloaded this logic program thing on my computer. its 2:19 AM and im bored.
*my answer is that zero(0) is also a number, so if the dinosaurs have no wrinkles then there cannot be 2 or more dinosaurs with the same number of wrinkles because they simply dont have any.
Applesauce!!
not bad, ashley, but you said yourself that zero is a NUMBER, so if 2 dinosaurs have 0 wrinkles, then they still have the same NUMBER of wrinkles. right?
there is 4001 dinosorse not 4000
there are no dinosorsers with skin on them so they can't have wrinkles
Ok check this out.
They want to know if we can assume something is a certainty, not a probability. The difference is whether or not they mean specifically 2 dinosaurs or at least two dinosaurs.
I think we can assume from everyone's arguments that it is certain that there will always be at least two dinos with a particular number of wrinkles.
It is POSSIBLE for exactly two dinos to have the same number of wrinkles but not a certainty, therefore we cannot assume it.
But I think I'm getting off the point here it's late and I haven't slept in days.
The fact that they ask specifically 50 wrinkles (not, say, 199) leads me to believe that the answer to this question lies in mathematical probability not logical reasoning alone.
But maybe it is as straightforward as it looks...YES
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