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Brain Teaser Part 2
Question

Hey Guys, this is the continuation of the Brain teaser from
http://forums.microsoft.com/samvaad/showpost.aspx?postid=1713357&siteid=43&sb=0&d=1&at=7&ft=11&tf=0&pageid=5
We continue here once again... many more questions to come....
Answers




Pouring water V.
Measure exactly 2 litres of water if you have:
1. 4 and 5litre bowls
2. 4 and 3litre bowls
Hey this is avery easy one, specially for the people who havent been trying their hands on it...
@ Adnan, Arijit and Raghuram, please wait till the 1pm tommorow, then post the answer... lets see if anyone else can answer it.. its the simplest one yet.. if you have been observing the previous questions and answers, you can easily answer this... 


@Varun, Well I did post after 1:00 pm.
Soln 1:
1) Fill the 5litre bowl
2) Fill the 4litre bowl from the 5litre bowl
3)Empty the 4litre bowl
4)Thus we have 1 litre in the 4litre bowl, now fill the 5litre bowl and pour it in the 4litre bowl (where there is already 1 litre).
5)Now you have 2 litres in the 5litre bowl.
Soln 2:
1) Fill the 3litre bowl and pour it into the 4litre bowl.
2) Fill the 3litre bowl again fill the 4litre bowl (Where there is 3litre remaining)
3) Thus you have 2 litres in the 3litre bowl. 

Hey don't say that...There is nothing wrong with you, Your rank and your point say everything.
It is just that your knack is at something else. I have never seen you falter at any of the pogramming threads.
Best of luck to you and my wishes that you may win this contest hands down. 
Hey Harshil, dont worry, you will get used to it after some practice.. just try this one out...
Pouring water VI. 
Imagine having three bowls. In the bowl A (8 litres capacity) are 5 litres of water. In the bowl B (5 litres capacity) are 3 litres of water. In the bowl C (3 litres capacity) are 2 litres of water.
Can you measure exactly 1 litre, pouring only 2 times? 

Well, no Harshil.. The question was to get exactly 'one' litre, not 2...
I think this will do (though I don't know whether to count the number of 'pourings' to be 2 or 3)..
* Pour a litre of water from 8 ltr bowl to 3 ltr bowl (pour till it gets filled) and discard the water in 3 ltr bowl.
=>Now 8 ltr bowl has 4 ltrs.
* Pour 3 ltrs from 8 ltr bowl to 3 ltr one.
=>Now 8 ltr bowl has 1 ltr.
Geez, I didn't use the 5 ltr bowl at all.. Probably there's a better solution.. 
Well, as i had not mentioned that you dont have to waste the water, you answer would be valid...
But lets put the condition that you are not suppose to waste the water, so now try to get 1ltr in 2 pouring....
@Harshil, dont worry, you got 2, now you will get 1 also.. try again... 




Let A be the 7minute sandclock and the other be B
1)Both the sandcolocks are allowed to start.
2)When all sand from B has fell into the lower chamber, immediately turn it upside down...
3)When all sand from A has fell into the lower chamber, immediately trun B upside down.
4)The count starts form then.. When sand has fell from one chamber of B to another, 1 minute would have passed by.. Turn it upside down immediately..
5)After another 4 minutes , the sand would have fell completley from one chamber to another.. Turn B upside down again..
6)When the sand has been transferred completley this time, 9 minutes would have passed by...
(Though more than 9 minutes would have passed due to the small delays caused in turning the sand clocks)

My calculations give me 18 minutes Raghu. Am I wrong somewhere?
>1)Both the sandcolocks are allowed to start.
>2)When all sand from B has fell into the lower chamber, immediately turn it upside down...
4 minutes over
>3)When all sand from A has fell into the lower chamber, immediately trun B upside down.
7 minutes over, B has 3 minutes' sand in upper chamber
>4)The count starts form then.. When sand has fell from one chamber of B to another, 1 minute
>would have passed by.. Turn it upside down immediately..
As I said, it seems 3 minutes, not 1 minute, would have passed by in this step. So totals to 10 already.
>5)After another 4 minutes , the sand would have fell completley from one chamber to another.. Turn
>B upside down again..
10+4 = 14
>6)When the sand has been transferred completley this time, 9 minutes would have passed by...
14+4 = 18

Ok guy, there was a small error in my previous answer.. Now, i'll post the corrected solution...
Let A be the 7minute sandclock and the other be B
1)Both the sandcolocks are allowed to start.
2)When all sand from B has fell into the lower chamber, immediately turn it upside down...(3 minutes of sand remaining in A)
3)When all sand from A has fell into the lower chamber, start the count... (1 minute of sand remaining in B)
4) When sand has fell from one chamber of B to another, 1 minute would have passed by.. Turn it upside down immediately..
5)After another 4 minutes , the sand would have fell completley from one chamber to another.. Turn B upside down again..
6)When the sand has been transferred completley this time, another 4 minutes would have passed by...
Now B's timing after A's completition is 1+4+4 =9 minutes
(Though more than 9 minutes would have passed due to the small delays caused in turning the sand clocks)

Oh.. I'm very sorry. I ignored the 'count starts from then' part as I couldn't understand what it meant.
While reading Raghu's answer, I got a somewhat simpler solution. But most of the work had been done by Raghu, so the credit for the answer goes to him I think.
1) Start both A(7 min) and B(4 min) (0 minutes over)
2) When B finishes (+4 min), turn it upside down
3) When A finishes (+3 min), turn A upside down
4) When B finishes (+1 min), turn A upside down
5) Allow A to finish (+1 min).
So 0+4+3+1+1 = 9 min.Hope I've not screwed up again...


Well guys, I had been talking to the owner of the site from where i m posting this questions..
I asked for his permission to post the questions from his site here in our forums, He gave the permission and asked to mention his site name....
So Special thanks to the brainden.com site owner for giving out such a wonderful questions...
Please do visit the site for new questions and get registered.. I will continue to post more questions from the site here, but will really like if you guys try to solve the problem on your own and do not refer to the site for the answer....
So once again Special thanks to
brainden.com
Its a wonderful site with lots of questions, and we will have a part of it here in the MS Forums...
So do visit the site.... (but not for answers to the questions posted here) 




Sandglass II.
A teacher of mathematics used an unconventional method to measure time for a test lasting 15 minutes. He used just a sandglass, which spills in 7 minutes and a second sandglass, which spills in 11 minutes. During the whole time he turned sandglasses only 3 times. Explain how the teacher measured 15 minutes.

Start the 7 min and 11 min sand glasses.
When the 7 min sand glass has stopped, start the timing procedure (That is how we will be able to get the measurement of 117 = 4 min).
After the 11 min one as finished, restart it again. Thus, with 4 min for prev one and 11 min now, we have mesaured 4+11= 15 min. 










Harshil_Patel_03b5f2 wrote: Actually i dont know what to do, can you please give one example, and solution of it with explanation ?
Ok, let me give the example of the one already soved above...
just imagine that the equation below is made of the matchsticks..
XI  V = IV
There will be 11 matchsticks used in the above equation....
Now you are suppose to move just one Matchstick, i.e. one stick from above to make the euqation correct...
XI  V = IV the equation means
11  5 = 4 Not correct...
I move one matchstick
IX  V = IV
9  5 = 4
Now the equation is correct... This way you are suppose to solve the questions.. now try out this one
X + V = IV 






@Harshil I was not refering to you
I said that making the equation as not equal to was not expected....
Okk.. there is one more answer to it.. its a bit tricky one but find out...
by then here is the new question...
As today is a special day, I will post a new question at a gap of 2 hrs...
So next question will be at 2pm...
1)
The following equation is made of 14 matches:
XIV  V = XX
2)
The following equation is made of 11 matches:
IX  IX = V
3)
The following equation is made of 12 matches:
X = VIII  II 




Shegoat, Wolf and Cabbage
A farmer is returning from market, where he bought a shegoat, a wolf and cabbage. On the way home he must cross a river. His boat is little, allowing him to take only one of the three things. He can't keep the shegoat and the cabbage together (because the shegoat would eat it), nor the shegoat with the wolf (because the shegoat would be eaten).
How shall the farmer get everything on the other side (without any harm)? 
* Take the goat and place him on the other side (leaving wolf and cabbage in side 1)
* Take the wolf and go to the other side, place the wolf and take back the goat.
* Place the goat on side 1, and take the cabbage to the other side (so goat is in side 1, wolf and cabbage are in side 2).
* Now take the goat to side 2.
Hope this is right...
All replies




Pouring water V.
Measure exactly 2 litres of water if you have:
1. 4 and 5litre bowls
2. 4 and 3litre bowls
Hey this is avery easy one, specially for the people who havent been trying their hands on it...
@ Adnan, Arijit and Raghuram, please wait till the 1pm tommorow, then post the answer... lets see if anyone else can answer it.. its the simplest one yet.. if you have been observing the previous questions and answers, you can easily answer this... 


@Varun, Well I did post after 1:00 pm.
Soln 1:
1) Fill the 5litre bowl
2) Fill the 4litre bowl from the 5litre bowl
3)Empty the 4litre bowl
4)Thus we have 1 litre in the 4litre bowl, now fill the 5litre bowl and pour it in the 4litre bowl (where there is already 1 litre).
5)Now you have 2 litres in the 5litre bowl.
Soln 2:
1) Fill the 3litre bowl and pour it into the 4litre bowl.
2) Fill the 3litre bowl again fill the 4litre bowl (Where there is 3litre remaining)
3) Thus you have 2 litres in the 3litre bowl. 

Hey don't say that...There is nothing wrong with you, Your rank and your point say everything.
It is just that your knack is at something else. I have never seen you falter at any of the pogramming threads.
Best of luck to you and my wishes that you may win this contest hands down. 
Hey Harshil, dont worry, you will get used to it after some practice.. just try this one out...
Pouring water VI. 
Imagine having three bowls. In the bowl A (8 litres capacity) are 5 litres of water. In the bowl B (5 litres capacity) are 3 litres of water. In the bowl C (3 litres capacity) are 2 litres of water.
Can you measure exactly 1 litre, pouring only 2 times? 

Well, no Harshil.. The question was to get exactly 'one' litre, not 2...
I think this will do (though I don't know whether to count the number of 'pourings' to be 2 or 3)..
* Pour a litre of water from 8 ltr bowl to 3 ltr bowl (pour till it gets filled) and discard the water in 3 ltr bowl.
=>Now 8 ltr bowl has 4 ltrs.
* Pour 3 ltrs from 8 ltr bowl to 3 ltr one.
=>Now 8 ltr bowl has 1 ltr.
Geez, I didn't use the 5 ltr bowl at all.. Probably there's a better solution.. 
Well, as i had not mentioned that you dont have to waste the water, you answer would be valid...
But lets put the condition that you are not suppose to waste the water, so now try to get 1ltr in 2 pouring....
@Harshil, dont worry, you got 2, now you will get 1 also.. try again... 




Let A be the 7minute sandclock and the other be B
1)Both the sandcolocks are allowed to start.
2)When all sand from B has fell into the lower chamber, immediately turn it upside down...
3)When all sand from A has fell into the lower chamber, immediately trun B upside down.
4)The count starts form then.. When sand has fell from one chamber of B to another, 1 minute would have passed by.. Turn it upside down immediately..
5)After another 4 minutes , the sand would have fell completley from one chamber to another.. Turn B upside down again..
6)When the sand has been transferred completley this time, 9 minutes would have passed by...
(Though more than 9 minutes would have passed due to the small delays caused in turning the sand clocks)

My calculations give me 18 minutes Raghu. Am I wrong somewhere?
>1)Both the sandcolocks are allowed to start.
>2)When all sand from B has fell into the lower chamber, immediately turn it upside down...
4 minutes over
>3)When all sand from A has fell into the lower chamber, immediately trun B upside down.
7 minutes over, B has 3 minutes' sand in upper chamber
>4)The count starts form then.. When sand has fell from one chamber of B to another, 1 minute
>would have passed by.. Turn it upside down immediately..
As I said, it seems 3 minutes, not 1 minute, would have passed by in this step. So totals to 10 already.
>5)After another 4 minutes , the sand would have fell completley from one chamber to another.. Turn
>B upside down again..
10+4 = 14
>6)When the sand has been transferred completley this time, 9 minutes would have passed by...
14+4 = 18

Ok guy, there was a small error in my previous answer.. Now, i'll post the corrected solution...
Let A be the 7minute sandclock and the other be B
1)Both the sandcolocks are allowed to start.
2)When all sand from B has fell into the lower chamber, immediately turn it upside down...(3 minutes of sand remaining in A)
3)When all sand from A has fell into the lower chamber, start the count... (1 minute of sand remaining in B)
4) When sand has fell from one chamber of B to another, 1 minute would have passed by.. Turn it upside down immediately..
5)After another 4 minutes , the sand would have fell completley from one chamber to another.. Turn B upside down again..
6)When the sand has been transferred completley this time, another 4 minutes would have passed by...
Now B's timing after A's completition is 1+4+4 =9 minutes
(Though more than 9 minutes would have passed due to the small delays caused in turning the sand clocks)

Oh.. I'm very sorry. I ignored the 'count starts from then' part as I couldn't understand what it meant.
While reading Raghu's answer, I got a somewhat simpler solution. But most of the work had been done by Raghu, so the credit for the answer goes to him I think.
1) Start both A(7 min) and B(4 min) (0 minutes over)
2) When B finishes (+4 min), turn it upside down
3) When A finishes (+3 min), turn A upside down
4) When B finishes (+1 min), turn A upside down
5) Allow A to finish (+1 min).
So 0+4+3+1+1 = 9 min.Hope I've not screwed up again...


Well guys, I had been talking to the owner of the site from where i m posting this questions..
I asked for his permission to post the questions from his site here in our forums, He gave the permission and asked to mention his site name....
So Special thanks to the brainden.com site owner for giving out such a wonderful questions...
Please do visit the site for new questions and get registered.. I will continue to post more questions from the site here, but will really like if you guys try to solve the problem on your own and do not refer to the site for the answer....
So once again Special thanks to
brainden.com
Its a wonderful site with lots of questions, and we will have a part of it here in the MS Forums...
So do visit the site.... (but not for answers to the questions posted here) 




Sandglass II.
A teacher of mathematics used an unconventional method to measure time for a test lasting 15 minutes. He used just a sandglass, which spills in 7 minutes and a second sandglass, which spills in 11 minutes. During the whole time he turned sandglasses only 3 times. Explain how the teacher measured 15 minutes.

Start the 7 min and 11 min sand glasses.
When the 7 min sand glass has stopped, start the timing procedure (That is how we will be able to get the measurement of 117 = 4 min).
After the 11 min one as finished, restart it again. Thus, with 4 min for prev one and 11 min now, we have mesaured 4+11= 15 min. 










Harshil_Patel_03b5f2 wrote: Actually i dont know what to do, can you please give one example, and solution of it with explanation ?
Ok, let me give the example of the one already soved above...
just imagine that the equation below is made of the matchsticks..
XI  V = IV
There will be 11 matchsticks used in the above equation....
Now you are suppose to move just one Matchstick, i.e. one stick from above to make the euqation correct...
XI  V = IV the equation means
11  5 = 4 Not correct...
I move one matchstick
IX  V = IV
9  5 = 4
Now the equation is correct... This way you are suppose to solve the questions.. now try out this one
X + V = IV 






@Harshil I was not refering to you
I said that making the equation as not equal to was not expected....
Okk.. there is one more answer to it.. its a bit tricky one but find out...
by then here is the new question...
As today is a special day, I will post a new question at a gap of 2 hrs...
So next question will be at 2pm...
1)
The following equation is made of 14 matches:
XIV  V = XX
2)
The following equation is made of 11 matches:
IX  IX = V
3)
The following equation is made of 12 matches:
X = VIII  II 




Shegoat, Wolf and Cabbage
A farmer is returning from market, where he bought a shegoat, a wolf and cabbage. On the way home he must cross a river. His boat is little, allowing him to take only one of the three things. He can't keep the shegoat and the cabbage together (because the shegoat would eat it), nor the shegoat with the wolf (because the shegoat would be eaten).
How shall the farmer get everything on the other side (without any harm)? 
* Take the goat and place him on the other side (leaving wolf and cabbage in side 1)
* Take the wolf and go to the other side, place the wolf and take back the goat.
* Place the goat on side 1, and take the cabbage to the other side (so goat is in side 1, wolf and cabbage are in side 2).
* Now take the goat to side 2.
Hope this is right...


Dark Phobia
One family wants to get through a tunnel. Dad can make it in 1 minute, mama in 2 minutes, son in 4 and daughter in 5 minutes. Unfortunately, through the tight tunnel can go at once not more than two persons moving at the speed of the slower one.
Can they all make it if they have a torch that lasts only 12 minutes and they are afraid of the dark? 








The main reason for the manhole covers to be in circular shape is to prevent the cover from slipping into the hole..
Suppose the hole was a square one, then the lid can be slipped in by putting it vertically along the diagonals of the square.. Whereas such thing cannot happen in a circular manhole.. 

The Barbershop Puzzle
A traveler arrives in a small town and decides he wants to get a haircut. There are only two barbershops in town  one on East Street and one on West Street. The East Street barbershop is a mess, and the barber has the worst haircut the traveler has ever seen. The West Street barbershop is neat and clean, its barber's hair looks as good as a movie star's.
Which barbershop does the traveler go to for his haircut, and why? 
Well...It is a fact that, no Barber cuts his/her own hair. Hence, if there are only 2 barbers in town, they have to cut each others hair. The West Street Barber has done a bad job on the orther one, but the East Street Barber has done a good job. Hence, the customer should go to the East Street Barber.






















Chandru was very fond of biscuits. So his mom made 3 bottles of biscuits:
1 containing cream biscuits alone
1 containing salt biscuits alone
1 containing both types of biscuits
She prepared labels for the bottles: 'Cream', 'Salt' and 'Mixed'. Fixing her concentration on the IndiaEngland match, she placed the wrong labels on all the bottles...
She told Chandru about this, and asked him to find which bottle contains what.
* Chandru is not allowed to look inside the bottles.
* He can only take one biscuit from one of the bottles and taste it.
With that, he has to identify all the 3 bottles correctly...
Is it possible? Can you help him? 
Nice one... But its easy.. it can be done in one step only....
Pick up a biscuit from the jar labled as MIX
Now as all the jars are marked incorrectly.. That jar can not be a mixed one... so if you get a cream buscuit than its the jar with cream buscuits only and the other way round....
so let us consider we get a cream buscuit...
Label : S C M
Jars : C
Now as other jars are also marked incorrectly, The jar marked as the cream buiscuit has either mixed or salted.....
If it has mixed then
Label : S C M
Jars : M C
Then the jar marked as salted has salted buscuit, which is correct and so not possible...
So the jar marked as salted has Mixed and jar marked as Cream has Salted buscuits...
Label : S C M
Jars : M S C
We considered the mix jar to have Cream.. if its salt than ans would be
Label : S C M
Jars : C M S
It was a nice one.. let more come in,....