Two more puzzles

[Neeyik]

IIRC, no bird urinates....they just "ploop"

 

[Simon F]

Same as reptiles - they've only got the multi-purpose cloaca.

 

[nelg]

I still think that my original solution is the best. You get the answer and dinner, albeit a little well done.

 

[akira888]

I think the answer goes like this. Take 1 nut from the first bag, 2 nuts from the second, all the way up to 5 nuts from the fifth bag. Measure these 15 nuts (keeping track of which bag you draw x nuts out of).

Total
Weight Peanuts in bag "x"
15.1g _____ 1
15.2g _____ 2
15.3g _____ 3
15.4g _____ 4
15.5g _____ 5

 

[StefanS]

That's nearly there... Take heavy water, feed it to the chicken. Wait till the chicken takes a piss. Measure the amount of heavy water (tritiumO2) and the amount of piss.

inital amount of heavy water /Water in chicken=amount of (heavy water + amount of its byproducts)/ amount of water in piss

Simon F is the winner...

Not to burst your bubble, but chickens don't piss.

It doesn't matter if it's piss or shit as long you know the amount of water / heavy water...

 

[Xmas]

No... sand grains are particles; constant flow refers to kg/(m²s) ----> same mass in the air; however as all grains have different size and weight, microscopically no equilibrium can be reached since the process is statistically random. It just depends on how accurate your scale is...

"Constant" processes in physics always imply the presence of insignificant noise. Just as the "constant flow" is not really constant (the sand grains that add to the flow at the top of the hourglass are not exactly the same size as those that hit the bottom at the exact same time)

 

[Xmas]

A new puzzle: This is one from one of my colleagues....

A large smooth circular metal ring is standing upright on the ground. Two very heavy weights, which are designed to slide around the ring, are positioned at the top of the ring. I'll try to draw a diagram:

   -WW-  
  /    \
 /      \
|        |
 \      /
  \    /
   ----
----------Ground---

The weights are initially held at the top and then released. What happens?

Assuming the weights are equal:
In theory, because of the symmetry both weights should have no effect at all on the ring in horizontal direction, except for a bit of deformation because of centripetal force. Depending on how elastic the metal ring is, it might start to jump up and down.
In practise however I would expect the ring to start turning in one direction because there's always a bit of randomness.

 

[MfA]

I would guess he is looking for the answer that it will start spinning because of the coriolis force but without a pivot point, and some distance to the floor, all that will happen is that it will either topple or have the weights come to rest on the floor stopping any further motion.

One of my favourite riddles is this one :

A pirate ship captures a treasure of 1000 golden coins. The treasure has to be split among the 5 pirates: 1, 2, 3, 4, and 5 in order of rank. The pirates have the following important characteristics: infinitely smart, bloodthirsty, greedy. Starting with pirate 5 they can make a proposal how to split up the treasure. This proposal can either be accepted or the pirate is thrown overboard. A proposal is accepted if and only if a majority of the pirates agrees on it. What proposal should pirate 5 make?

(I like it because I always liked proofs by induction in math.)

 

[akira888]

Measure the amount of heavy water (tritiumO2) and the amount of piss.

[pedantic] Actually the majority of heavy water molecules are Deuterium Oxide (hydrogen-2). [/pedantic]

 

[Xmas]

One of my favourite riddles is this one :

A pirate ship captures a treasure of 1000 golden coins. The treasure has to be split among the 5 pirates: 1, 2, 3, 4, and 5 in order of rank. The pirates have the following important characteristics: infinitely smart, bloodthirsty, greedy. Starting with pirate 5 they can make a proposal how to split up the treasure. This proposal can either be accepted or the pirate is thrown overboard. A proposal is accepted if and only if a majority of the pirates agrees on it. What proposal should pirate 5 make?

I think this puzzle is flawed. I guess the correct answer should be "all gold to 5", but it doesn't work out. 3 will get all the gold, 4 and 5 will die. Simply because 1 will never accept and 2 will only accept any proposal from 3 because he will die if he does not. 3 knows this and will reject any proposal from 4 and 5, so those two will never have a majority.

 

[MfA]

No it isnt flawed, just consider my hint some more.

 

[Xmas]

No it isnt flawed, just consider my hint some more.

Then show me where my conclusion is wrong.

Actually, I found a "solution", but it requires knowledge on how much the pirates put greed over bloodthirst. Pirate 5 proposes to give part of the gold to 2 and keeps the rest for himself. This way 2 *might* accept the proposal, 4 must accept it else he will die, too, and 5 obviously accepts it.

 

[Nathan]

How about this, MfA?

If we assume pirates 5 through 3 have their proposals get rejected, then 2 is screwed because 1 will reject any proposal other than all 1000 coins going to him. So 2 must vote for 3's proposal inorder to get some of the loot.
3 now has the power and can offer 2 a paltry 1 coin (which is better than none) and keep 999 for himself. Obviously 2 wants more than one coin, so he must actually accept pirate 4's proposal.
4 can offer pirate 2 two coins, and pirate 1 one coin, which is better than either of them will get from pirate 3, but is still pretty pathetic.
So now 1 and 2 want to accept pirate 5's offer. 5 can offer pirate 1 two coins and pirate 2 three coins and keep the rest for himself

Edit: This obviously assumes that higher ranked pirates don't have to get more than lower ranked ones. It's not particularly clear from your post if this is actually the case.

 

[akira888]

Nathan:

Couldn't pirate 5 buy pirate 3 with only one coin (since he'll get nothing with pirate 4's plan) along with pirate 1 with two coins?

 

[MfA]

Almost Nathan, but 1 is blood thirsty, he wont accept any proposal from 2 because he doesnt need to ... so 3 can just propose to give everything to himself which will save 2 a swim ... in the end 5 has to give 2 coins to either 1 or 2 and 1 coin to 3.

 

[Nathan]

Ah well, close enough.

 

[Xmas]

Almost Nathan, but 1 is blood thirsty, he wont accept any proposal from 2 because he doesnt need to ... so 3 can just propose to give everything to himself which will save 2 a swim ... in the end 5 has to give 2 coins to either 1 or 2 and 1 coin to 3.

I see no reason why 5 should give 3 a coin. 1 or 2 will only accept if their greed is bigger than their bloodthirst, which is not mentioned. Like I mentioned earlier. That's why the puzzle is flawed.

 

[StefanS]

Measure the amount of heavy water (tritiumO2) and the amount of piss.

[pedantic] Actually the majority of heavy water molecules are Deuterium Oxide (hydrogen-2). [/pedantic]

The thing is you don't use Deuterium since it's not radioactive, which makes it unpractical for quantifying the amount of the initial water sample...
I just called it heavy water since I know no better name for it in English... except TritiumO2.....

 

[StefanS]

This one is easy and pretty well known problem:

A 2-d dimensional physicist lives in his little house in his little two dimensional world. But one he decides he wants to know, if his world is flat (infinite plane) or not (plane of a torus) and all he got, apart from a nagging wife, is a lousy ball of wool.

 

[Simon F]

This one is easy and pretty well known problem:

A 2-d dimensional physicist lives in his little house in his little two dimensional world. But one he decides he wants to know, if his world is flat (infinite plane) or not (plane of a torus) and all he got, apart from a nagging wife, is a lousy ball of wool.

Surely you mean a disc of wool? I'm almost loathe to ask this but, how long is the piece of string?

AHH. If he's a mathematician, I can think of a way of doing it but it might require the assumption of other properties/abilities. The angles of a triangle on a plane add to 180 degrees, but not on a curved surface. If he formed a very large triangle with his string and measured the angles...



I don't think anyone has given a satisfactory answer to the weights on the ring problem (and yes they are equal in mass).