The Chicken From Minsk Thread

[Aircraft Aviation 2]

Interestingly, alot of the later problems are nothing like these. There is a fair bit of variety.

 

@John: These are, of course, just the warm up questions. However, I can confirm that British Unis at least are using these types of questions; most respected University level Physics/Maths courses require an interview. Having recently undergone one of these interviews with another in just over a week, I can confirm the majority of the interview questions are logic based and require you to think on your feet; nothing to do with Physics or Maths directly. The Universities want you to be able to cope with new, alien concepts without reliance upon plugging numbers into formulae. But trust me, they get harder. If only you could see problem #99 .

 

These particular questions were used to test first year intercourse students at MIT in the 80s and early 90s. In fact, the book was written by Robert M Rose from MIT; it's simply that the origin of the questions lies within Russia.

[Quickmarch 488]

OK - No boatman, therefore: One page gets to drown

 

It can be made to work provided the overlap at trip 4 while unloading/loading the boat is OK. An island in the middle would be a big help.

 

Start      K1 P1 K2 P2 K3 P3 Start bank side

 

Trip 1                 K3 P3

Return1              K3

 

Result:    K1 P1 K2 P2 K3  Start bank side

                                    P3  End Bank side

          

Trip 2                K2 P2

Return2             K2

 

Result:    K1 P1  K2    K3  Start bank side

                          P2    P3  End Bank side

             

Trip 3      K1 P1

Return3   K1

 

Result:     K1 K2 K3 Start bank side

                P1 P2 P3 End Bank side

             

 

Trip 4      K1 K2

Return4             P3 

 

Result:           K3 P3  Start bank side

            K1 P1 K2 P2 End Bank side

             

 

Trip 5       K3 P3

 

Result:     K1 P1 K2 P2 K3 P3 End Bank side

 

[Aircraft Aviation 2]

 

OK - No boatman, therefore: One page gets to drown

 

It can be made to work provided the overlap at trip 4 while unloading/loading the boat is OK. An island in the middle would be a big help.

 

Start      K1 P1 K2 P2 K3 P3 Start bank side

 

Trip 1                 K3 P3

Return1              K3

 

Result:    K1 P1 K2 P2 K3  Start bank side

                                    P3  End Bank side

          

Trip 2                K2 P2

Return2             K2

 

Result:    K1 P1  K2    K3  Start bank side

                          P2    P3  End Bank side

             

Trip 3      K1 P1

Return3   K1

 

Result:     K1 K2 K3 Start bank side

                P1 P2 P3 End Bank side

             

 

Trip 4      K1 K2

Return4             P3 

 

Result:           K3 P3  Start bank side

            K1 P1 K2 P2 End Bank side

             

 

Trip 5       K3 P3

 

Result:     K1 P1 K2 P2 K3 P3 End Bank side

 

 

Good attempt John!

 

The first step (trip 1) is entirely correct. However, a problem arises in trip 2. Here, you bring K2 and P2 across, which means that, momentarily, K2 will be on the same side as P3, which will kill our poor P3!

 

Remember, there's nothing stopping two pages going across in the boat together. The only restriction is that a page cannot be left alone if he has to stand next to a Knight that isn't his own master.

[Quickmarch 488]

I was sort of thinking that as long as the Knight didn't get out of the boat there'd be no conflict. However, the whole premise falls apart at trip 4 where a Page has to replace a Knight in the boat. 

 

Trip 4      K1 K2

Return4             P3

 

Gonna take a bit more beer.

[Aircraft Aviation 2]

Hi John,

 

Yes I suppose the question is (perhaps purposefully) trickily worded.

 

All in all, a page can not be on the same side (whether in or out of the boat) as the other knights unless his own Master is present. He can, however, be on a side by himself, or be on a side consisting only of pages.

[stu7708 244]

Ok. Let's give this a try

 

Trip 1:  K3, P3

Return K3

 

Result

K1, K2, K3, P1, P2 start side

P3 end side

 

Trip 2: P1, P2

Return P1

 

Result

K1, P1, K2, K3 start side

P2, P3 end side

 

Trip 3: K2, K3

Return: K2, P2

 

Result

K1, P1, K2, P2 start side

K3, P3 end side

 

Trip 4: K1, K2

Return: P3

 

Result

P1, P2, P3 start side

K1, K2, K3 end side

 

Trip 5: P1, P2

Return: P1, P2 or K3, 

 

Assuming K3 resulting in 

K3, P3 start side

K1, P1, K2, P2 end side

 

Final trip: K3, P3 and all of them are at their destination...

[Quickmarch 488]

Looks good to me, Mikael. Let's see what the originator says.

[Aircraft Aviation 2]

Micke; absolutely perfect! Well done! Thanks for taking the time to answer too . Also thanks for your participation in this question John!

 

Unless anyone is particularly bothered, we'll skip problems #6 and #7 since they are the same as #5, except involving an island and four pairs of knights (respectively). 

 

Problem #8 will follow shortly.

[Aircraft Aviation 2]

Problem #8

 

Grandfather's Breakfast - Grandfather is a very-hard boiled customer. In fact, his eggs must be boiled for exactly 15 minutes, no more, no less. One day he asks you to prepare breakfast for him, and the only timepieces in the house are two hourglasses. The larger hourglass takes 11 minutes for all the sand to descnd; the smaller, 7 minutes. What do you do? (Grandfather grows impatient!)

 

I think this required some thought, but is undoubtedly much "shorter" than problem #5.

[J G 927]

I think i can do this one..

1. Start both timers.  

2. When the 7 min one runs out start boiling the eggs.

3. The 11 min timer will run for a further 4 mins.

4. Turn over the 11 min timer as soon as it ends and run for a full 11 mins 

5. When it runs out stop boiling the eggs.

 

4+11 = 15 QED

[jaydor 345]

Just beat me  John, I was: 11-7 = 4+11 =15

[Aircraft Aviation 2]

John, that's absolutely correct.

 

There are actually two solutions to this; yours is the more inefficient one (no offense intended!). Although interestingly, the book lists your solution as the first answer, and then the more efficient one as a secondary answer. This is how I did it (if you're interested):

 

1.) Start both timers, and put the eggs in at the same time

2.) When the 7 minute one runs out, turn it immediately back over

3.) When the 11 minute one runs out, there will be 4 minutes worth of time in the 7 minute timer

4.) Flip the 7 minute timer (actually a "4 minute timer" here)

5.) When the 7 minute timer runs out (for the second time); that's 15 minutes

 

This method is a wee bit more efficient since it takes less time; exactly 15 minutes as opposed to 22 (remember, Grandfather grows impatient!). Nonetheless however, your answer is still perfectly valid. Well done!

[Aircraft Aviation 2]

Problem #9

 

The Prisoner and the Guards - You are a prisoner with two guards, each guarding one door to your cell. One guard always lies and one is always truthful, but you do not know which is which. You may leave your cell by one of two doors. One door leads to the execution block and death. The other leads to freedom. You may ask only one question, which you may address to either of the guards but not to both. What do you do?

 

I can see this causing similar conflict to Problem #4... Oh well, we're almost out of the warm up problems now anyway.

[mutley 4,498]

Ask each guard what the other guard will tell you to which door to open to save yourself? They both know which is the door to execution, so.. (Let's say it is door 1)

 

The good guard will always tell you that the lying guard will tell you to go down the door to execution.  (Door 1)

 

The lying guard will always tell you that the truthful guard will send you down the door to execution. (Door 1)

So, as they both know which is the door to execution, you have to choose the door they did not say, the job's a goodun?.. Door 2?

[Aircraft Aviation 2]

Spot on Joe, I have to admit when I first read this I was going down completely the wrong path (if you'll pardon the pun). Another one for your tally!

[Aircraft Aviation 2]

Problem #10

 

Ivanov and the Clock - Ivanov is looking for his boss. Ivanov's boss is a Party functionary, and his office is luxurious, with soft furniture, thick carpeting on the floors, heavy draperies on the walls, and a thick, tightly closed, soundproof door. Usually, he is not in. Ivanov opens the door to his boss' office and hears the wall clock strike once. The boss is not there. Ivanov leaves the door open. A half-hour later, Ivanov is astonished to hear the clock strike once, again. After another half-hour, this experience is repeated; still, no boss. Now Ivanov, losing patience, waits another half hour and hears the clock strike only once for the fourth time. The boss's secretary, who has now returned, tells Ivanov that the boss left for lunch shortly before Ivanov arrived for the first time. Ivanov knows that the clock strikes the number of hours on the hour, and strikes just once every half-hour. When is the latest that the boss could have left his office?

[mutley 4,498]

Does he come in before the last strike of 12?

Then 12:30

Then 1:00

Then 1:30 ?

 

So is the answer 11:59?

 

 

[Aircraft Aviation 2]

Right again Joe! The answer is indeed before the last strike of 12 (but obviously after the 11th strike). 

 

Technically, "11:59" isn't correct, because we don't know the time period between strikes when it's striking for an hour (in other words, what is the time gap between the 12 strikes? 1 second? 5 seconds?). Or, in other words, we don't know enough information to give a degree of precision to the nearest minute; all we know is that it was "sometime before 12" (although reasonably one could assume, yes, that it will be 11:59 and X seconds). Anyway, I'm rabbiting on, "before the 12th strike" is of course correct (the book actually states an answer of 12:00PM). Well done Joe!

 

 

[Aircraft Aviation 2]

Problem #11

 

Shopping with Boris and Marina - Boris and Marina want to buy ice cream bars. However, Boris is 24 kopeks short of the price of a bar, and Marina is 2 kopeks short. They decide to pool their funds and buy a single bar. When they do, they still do not have enough money. How much does an ice cream bar cost?

[mutley 4,498]

Wild guess, 25 Kopeks? 

[Aircraft Aviation 2]

Right you are again Joe . You can tell these are the warm up questions!

[Aircraft Aviation 2]

Problem #12

 

Shopping with Boris and Marina, Part II - Boris and Marina are shopping again, this time for chocolate bars. Boris observes, "If I add half my money to yours, it will be enough to buy two chocolate bars". Marina naively asks, "If I add half my money to yours, how many can we buy?". Boris replies, "One chocolate bar". How much money did Boris have?

[J G 927]

Boris has no money.

 

Say a chocolate bar costs 50p

 

If Boris has no money and Marina has £1

 

then 1/2 x £0 = £0

£1 + £0 = £1 or 2 bars

 

and 1/2 x £1 = 50p

£0 +50p = 50p or 1 bar

[Aircraft Aviation 2]

Affirm John, Boris is clearly a cheapskate! Another to add to your tally, good job.

[Aircraft Aviation 2]

Problem #13

 

At the Movies - Olya, Petia, Kolia and Klava regularly attend the movies on school days, usually on days when they wish to avoid an assignemtn. They began going together on one rainy day, and then went regularly but on different schedules. Olya went every frouth day; Petia every fifth day; Kolia every seventh day; and Klava every ninth day. When will they again all go together to the movies? Give your answer in days after their first visit.

 

First bit of maths starting to trickle in...