The Chicken From Minsk Thread

[allardjd 1,853]

Problem #9 - Prisoner and Guards
 

You may ask only one question, which you may address to either of the guards but not to both

 

 

Ask each guard what the other guard will tell you to which door to open to save yourself?

 

 

Ahem....

 

John

[allardjd 1,853]

#13 - 1,260th day, unless the condition of only going on school days remains in force.  Since it says they now "go regularly" I'm assuming that condition no longer applies.

 

John

[Aircraft Aviation 2]

Problem #9 - Prisoner and Guards

 

You may ask only one question, which you may address to either of the guards but not to both

 

 

Ask each guard what the other guard will tell you to which door to open to save yourself?

 

 

Ahem....

 

John

 

I'm assuming Joe meant ask a guard what the other guard would say is the right door, which is indeed correct. You'd always go for the door they don't tell you to go down.

[Aircraft Aviation 2]

Perfect John, it is indeed 1,260 days later. This is the product of 4 x 5 x 7 x 9.

 

[Aircraft Aviation 2]

Problem #14

 

A Drinking Problem - Besides chess playing and problem solving, drinking is and always has been the most common form of recreation in Russia. Vassily has acquired a 12-liter bucket of vodka and wishes to share it with Pyotr. However, all Pyotr has is an empty 8-liter bottle and an empty 5-liter bottle. How can the vodka be divided evenly?

 

Not too hard I hope!

[J G 927]

If 12 litre bottle is x

8 litre bottle is y

5 litre bottle is z

1. Fill y with vodka

so x=4 Y= 8 Z = 0

2. Fill z from y

so x=4, y=3 z=5

3. Empty z into x

so x=9 y=3 z=0

Empty y into z

so x=9 y=0 z=3

Fill y from x

so x =1 y=8 z=3

Top up z from y

so x=1 y=6 z=5

1 man takes x and z (6 litres) the other takes y (6 litres) QED

[Aircraft Aviation 2]

Perfect once again John, not too hard eh?

[Aircraft Aviation 2]

Problem #15

 

The Caterpillar - It is spring, and there are 12 hours of daylight. A caterpillar climbs a vertical wall at a speed of 1 foot per hour during the day, and then sleeps for the 12 hours of darkness, during which it slides downward at 1/2 foot per hour. The wall is 48 feet high. How long will it take the caterpillar to reach the top of the wall?

[allardjd 1,853]

End Day 1 = 12 ft.
End Night 1 = 6 ft.
End Day 2 = 18 ft.
End Night 2 = 12 ft.
End Day 3 = 24 ft.
End Night 3 = 18 ft.
End Day 4 = 30 ft.
End Night 4 = 24 ft.
End Day 5 = 36 ft.
End Night 5 = 30 ft.
End Day 6 = 42 ft.
End Night 6 = 36 ft.
End Day 7 = 48 ft.

[Aircraft Aviation 2]

Well done John!

[Aircraft Aviation 2]

Problem #16

 

Wsahing Your Face - Is it possible to wash your hands with liquid nitrogen (77K) without harm? Explain how this can occur.

 

Just to make it clear; the book wants a solution that utilizes no other equipment apart from your face and the liquid nitrogen itself. I can feel a whole range of suggestions arriving here, so to score, you must get the solution the book provides (which, to be honest, is the only real realistic solution anyway).

[J G 927]

Washing you hands with liquid nitrogen is going to give you sever frost bight if you just dip your hands in and go for it. So that cant be the answer...... or can it?

 

To pull this off you must dip your hands into the liquid nitrogen for less than one second. This rapid immersion will protect your hands because of the Leidenfrost effect which causes an insulating layer of vapour to be formed around your hands. but it only lasts a fraction of a second, so beware, hesitate and you will loose some fingers! 

[Aircraft Aviation 2]

That'll do nicely John . I'm sort've glad this one was over quickly!

[Aircraft Aviation 2]

Problem #17

 

Buying Berries - Berries (many of which resemble cranberries) are popular in Russia. In one warehouse, 1,000kg of fresh berries are stored. The berries contained 99% water when fresh, but a few days later, a test showed that there was now only 98% water, due to the drying out of the berries. What do the berries weigh now?

[allardjd 1,853]

Then:

Berries: 10 Kg (1%)
Water:  990 Kg (99%)
Total:  1,000 Kg (100%)

 

Now:

Berries: 10 Kg (2%)
Water:  490 Kg (98%)
Total:  5,000 Kg (100%)

 

EDIT: TYPO - Total is 500 Kg at the end....  JDA

[J G 927]

Start

Berries   10 kg 1% of weight

water    990 kg 99% of weight

total     1000kg 100% of weight

 

Now

Berries   10kg 2% of weight 

total      500kg 100% of weight (10 x 100/2)

 

Therefore 500 - 10 = 490

 

water weight = 490Kg

 

Edit.... John sneaked in there ahead of me...

[Aircraft Aviation 2]

I think we're nearing the end of the warm up questions! Good job John.

[Aircraft Aviation 2]

Problem #18

 

The Videotape -  Rewinding an entire videotape cassette, where the tape spindle rotates at constant angular velocity, takes 4 minutes. How long did it take to rewind the first 25% of the tape? For simplicity, assume that the diameter of the fully rewound tape reel is much greater than the diameter of the tape spindle.

[allardjd 1,853]

It approaches 1/2 asymptotically.

 

John

[Aircraft Aviation 2]

John, please could you clarify? Are you referring to 0.5 minutes?

[allardjd 1,853]

No, relative to total time.  For the four minute example, the first 25% would require approximately two minutes - slightly less since its asymptotic from below. It's a case of the faster it goes, the faster it goes.

 

John

[allardjd 1,853]

Wsahing Your Face - Is it possible to wash your hands with liquid nitrogen (77K) without harm? Explain how this can occur.

 

 

This rapid immersion will protect your hands because of the Leidenfrost effect which causes an insulating layer of vapour to be formed around your hands.

 

 

Just a technicality here, but if it's only vapor that's touching your hands, are you really washing them?  Would any cleaning be done?  I think "immerse" might be a better choice of words.  Are all Russian academics such imprecise thinkers, or is it the vodka?

 

By the way, Jack said "face" and John addressed "hands". 

 

John

[J G 927]

Is this a trick question?

 

In order to work properly an analogue recording device must be read at a constant speed. therefore the tape must pass the read head at a constant speed.

 

It follows that the time to reach to reach 25% of the way through is 1 min.  

 

As it does this the two spools will vary in speed as the circumference of one grows and the other diminishes, but the passage of tape past a point will be constant. 

 

John A, said "By the way, Jack said "face" and John addressed "hands". I did that is true but only the title of the question spoke of face, the questions words asked about hands.

 

Not well worded, and I agree that the premise of the answer is that the only way to do it is not to let the nitrogen touch your hands, not exactly washing.  More a magicians answer than a true one I guess! 

[Aircraft Aviation 2]

Is this a trick question?

 

In order to work properly an analogue recording device must be read at a constant speed. therefore the tape must pass the read head at a constant speed.

 

It follows that the time to reach to reach 25% of the way through is 1 min.  

 

As it does this the two spools will vary in speed as the circumference of one grows and the other diminishes, but the passage of tape past a point will be constant. 

 

John A, said "By the way, Jack said "face" and John addressed "hands". I did that is true but only the title of the question spoke of face, the questions words asked about hands.

 

Not well worded, and I agree that the premise of the answer is that the only way to do it is not to let the nitrogen touch your hands, not exactly washing.  More a magicians answer than a true one I guess! 

 

We're just rewinding the tape here. Not playing the tape. When playing the tape, the angular velocity of the reel changes with growing/decreasing diameter in order to maintain a constant read-rate. Indeed, this particular fact is actually mentioned in the answer "Note that the situation is different when the videotape is playing: now the tape velocity is constant and the angular velocities of both reel (accelerating) and bobbin (decelerating) will vary with time".

 

 

No, relative to total time.  For the four minute example, the first 25% would require approximately two minutes - slightly less since its asymptotic from below. It's a case of the faster it goes, the faster it goes.

 

John

 

This is correct. 

[hurricanemk1c 195]

Not quite sure about this - seems too like the 'Project Maths' we do at school - although at least you can see what you're trying to achieve in these questions!