Puzzle

Phæte said:
One I heard on the radio (?) at the bank yesterday:

I am the owner of a pet store that specializes in birds. If I put one canary per cage, I have one canary too many. But if I put two canaries per cage, I have one cage too many. How many canaries and cages do I have?
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4 canary and 3 cages?
 
thesubstitute said:
Correct :)


Next puzzle:

Imagine if you walk up a hill along the only path up on Monday. You started at 8 in the morning and reach the top at 5pm. Camped out at the top of the hill for the night.

Tuesday you decided to follow the same path down, and you start at 8am. Taking it easy, you stolled down and happened to arrive at the bottom exactly where you started at 5pm again.

Question is, were you at any point of on Tuesday at the same place along the path as you were on Monday at the same time?
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Assuming there is only one path then yes because if you imagine someone identical starting to walk up at the same time as you are starting walking down then at some point you are going to meet them and thus be in the same place at the same time as this "image" of you on the way up thus there must be a point when you would be in the same place at the same time on both days.

I think that makes sense :)

edit: ignore me, someone already gave this answer! (hopefully that means it is right)
 
thesubstitute said:
Another puzzle since the 2=1 one was immediately solved :<

This one will probably take some explaining along with answer! (yeah, please explain rather than just shouting out colour)

A king wants his daughter to marry the most logical of 3 intelligent princes, and so comes up with a test for them.

The princes are gathered into a room and seated, facing one another, and are shown 2 black hats and 3 white hats. They are blindfolded, and 1 hat is placed on each of their heads, with the remaining hats hidden in a different room.

The king tells them that the first prince to correctly identify the color of his hat will marry his daughter. A wrong guess will mean death.

The blindfolds are then removed. You are one of the princes, you see 2 white hats on the other prince's heads. What color is your hat?
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No where does it say you cant take your hat off and see it :D

thesubstitute said:
Correct :)


Next puzzle:

Imagine if you walk up a hill along the only path up on Monday. You started at 8 in the morning and reach the top at 5pm. Camped out at the top of the hill for the night.

Tuesday you decided to follow the same path down, and you start at 8am. Taking it easy, you stolled down and happened to arrive at the bottom exactly where you started at 5pm again.

Question is, were you at any point of on Tuesday at the same place along the path as you were on Monday at the same time?
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the beginning
 
Abraham said:
the plane is being pulled forward by the propellors/jet engines
the conveyor belt moving backwards just makes the wheels spin faster, it wont hold the plane back at all (apart from the friction involved)

the plane wouldnt lift straight up, it would just take off normally, but it would probably fall off the end of the conveyor first
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I'm never satisfied with this one. The question is generally phrased in a way that implies that the treadmill is acting in such a way that the plane is static. In which case presumably it can't take off.

But in actual case, the plane moves forward in spite of the fact that it is on a moving treadmill, and therefore would take of as expected.
 
tripitaka said:
I'm never satisfied with this one. The question is generally phrased in a way that implies that the treadmill is acting in such a way that the plane is static. In which case presumably it can't take off.
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Correct, if the plane is not moving with respect to the ground (actually the air) then it won't take off.

But in actual case, the plane moves forward in spite of the fact that it is on a moving treadmill, and therefore would take of as expected.
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Exactly.

The thread that someone linked is this exact case and it is clear that the plane will take off.

It is worded such that the treadmill is adjusted to match the speed of the plane. That means that as the plane moves forward (with respect to the ground) at 20mph then the treadmill is doing 20mph in the opposite direction. This just means that the wheels of the plane are rotating as if the plane was doing 40mph. But because the plane is still moving forward at 20mph then there is air passing over the wings and it will eventually take off.

If the normal take off speed for a plane (with repect to the ground) is 100mph. Then in this treadmill example, the plane will still take off when it is moving at 100mph (with respect to the ground). At this point the treadmill would be doing 100mph in the opposite direction and so the wheels would be spinning as if the plane was doing 200mph, but this is irrelevant.
 
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Sounds like the problem lies in the concept of how a plane moves forward, as to a car.

If a plane is "driven forward" by its wheels to generate lift to start with, in order to take off, then yeah - it can't take off on a conveyer belt. However it'd be silly for a plane to gain lift that way since as soon as it takes off the ground, the wheels won't be pushing the plane forward anymore and the plane will land again.

The point is that the plane is moving forward (during take off stage on the runway) by the thrust generated via the engines / propeller, which is why the wheels become irrelevant.

For those of us who have been on planes before, you just need to remember how the plane drives itself to the runway before take off, and then stops, before the engines roar madly...

Interesting puzzle that.
 
Anyone want to try another puzzle?

A king was hosting a banquet which will bring peace to many neighbouring countries, and he has imported 1000 bottles of wine from the various countries.

A week before the banquet, an informant told him that someone is trying to sabortage the banquet, by poisoning one of the bottles. A smallest amount of wine from the poisoned bottle will kill a person, but it'd take 6 days before the poison takes effect, and there're no symptoms before then.

The king's servants, being aware of the importance of this banquet, have all volunteered to help test the wine.

What is the least number of servants he had to use to find out which bottle is poisoned?


If you've already know the answer to this puzzle, please don't jump in and ruin it for everyone - I think it's a particularly satisfying puzzle to work out by yourself properly :)
 
Well I don't know the answer but I guess your going to have to break the 1000 bottles into groups of say 50 or 100 and then once someone dies from a particular group narrow it down.

So lets see, say 10 servants taste 100 allotted bottles each and once one dies you can rule out 900 bottles then give 11 bottles each the 9 remaining and see who dies and then split the bottles from the next dead person with the 8 survivors, then one would die and you would be pretty much there.

So the answer is less than 10, can anyone be bothered to work it out correctly?
 
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MookJong said:
Well I don't know the answer but I guess your going to have to break the 1000 bottles into groups of say 50 or 100 and then once someone dies from a particular group narrow it down.

So lets see, say 10 servants taste 100 allotted bottles each and once one dies you can rule out 900 bottles then give 11 bottles each the 9 remaining and see who dies and then split the final bottles with the 8, then you would know.

So the answer is less than 10, can anyone be bothered to work it out correctly?
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the problem is that you only have enough time for one round of testing..
 
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