Excellent Puzzles !!!

[gpta_varun]

O.k Guys , Now solve these ..............
Excellent Puzzles ....Let's see who solve these .................

one bottle out of 32 wine bottles is posioned with such poison that even
one drop
of it can kill a person.but any quantity of this poison kills exactly in
32 days.how will you find out the
bottle with poisoned wine using min number of taste testers in 32 days.
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in a multiple choice ques having 4 options, one is awarded 1 mark for
correct and -x for wrong ans.
if one answers randomply and get 0 marks find value of x.
(ans is considered correct only when one ticks all the correct options)
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a man spends 3 equal sums of money in purchasing doves,parrots and
peacocks.A parrot cost 1 rs more that
a dove.Had the man invested all his money in parrots,he would have been
able to
buy 2 parrots more that the number of peacocks he had purschased
earlier.also the man purchased 5 more
doves than parrots. the total sum of money he spent on purchasing the
birds is equal to 9 times
the total number of parrots he purchased. find the number of doves,
parrots and peacocks
he purchased and total minimum amount of money he spent.
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there is a chain of trianges whose vertices are metal beads. if the
sides of triangles
are formed by joining a single thread to the metal beads what will be
the length of the thread reqd. to form the chain
of 6 triangles of unit sides using 13 beads.
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I am in a 100-story building. I have with me two glass balls. I know
that if I throw the ball out of the window it will
never break if the floor number is less than F and it will always
break if the floor number is equal or greater than F.
Assuming that I can reuse the glass ball which didn't break, what is
the minimum number of throws required to find F and
the strategy to find F?
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One day two mathematicians, Igor and Pavel, meet in the street.
"I have three sons," says Pavel. "The product of their ages is equal to
36." Looking around and then
pointing to a nearby house, Pavel says, "The sum of their ages is
equal to the number of windows in the building over
there."
Igor thinks for a minute and then responds, "Listen, Pavel, I cannot
find the ages of your sons."
"Oh, I am very sorry", says Pavel; "I forgot to tell you that my
oldest son has red hair."
Now Igor is able to find the ages of the brothers. Can you do it?
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The Beatles have to be at a concert across the river in 17 minutes. The
problem is that the
bridge across the river is very weak and is strong enough to hold only
two people at a time
(only two people can cross at a time). They have only one flashlight
and anybody crossing
the river must have the flashlight at all times. John can cross the
bridge in 1 minute, Paul
needs 2 minutes, George needs 5 minutes and Ringo needs 10. can they
make it to the concert in time? If so, how?
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Mr Smith and Mr Jones are two maths teachers, who meet up one day. Mr
Smith lives in a house with a number
between 13 and 1300. He informs Mr Jones of this fact, and challenges

Mr Jones to work out the number by asking closed questions.
Mr Jones asks if the number is bigger than 500. Mr Smith answers, but
he lies.
Mr Jones asks if the number is a perfect square. Mr Smith answers, but
he lies.

Mr Jones asks if the number is a perfect cube. Mr Smith answers and
(feeling a little guilty) tells the
truth for once.

Mr Jones says he knows that the number is one of two possibilities, and
if Mr Smith just tells him
whether the second digit is 1, then he'll know the answer.

Mr Smith tells him and Mr Jones says what he thinks the number is. He
is, of course, wrong.
What is the number of Mr Smith's house

Best Regards

Varun

[JJ___]

The Beatles have to be at a concert across the river in 17 minutes. The
problem is that the
bridge across the river is very weak and is strong enough to hold only
two people at a time
(only two people can cross at a time). They have only one flashlight
and anybody crossing
the river must have the flashlight at all times. John can cross the
bridge in 1 minute, Paul
needs 2 minutes, George needs 5 minutes and Ringo needs 10. can they
make it to the concert in time? If so, how?

You never said how wide or deep the river was. So either they cross the river through it or they throw the torch back to each other. :p

[server_crash]

one bottle out of 32 wine bottles is posioned with such poison that even
one drop
of it can kill a person.but any quantity of this poison kills exactly in
32 days.how will you find out the
bottle with poisoned wine using min number of taste testers in 32 days.
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Alright, I came up with two solutions:

First, you could only have 1 person testing the wine, and that would be the person whom poisoned it. The one he didn't drink is the poisoned bottle.

Second, you would use 31 testers. If any of them died, you would know what bottle was poisoned. If no one died then you would know that it's the 32nd bottle.

[server_crash]

Was I correct?

[belama]

Your second answer makes sense... but the first might not work if all the bottles are the same and all shuffled. He wouldnt know which not to take.

[Rooju]

For the wine bottle puzzle.. I think I can do it with 9 tasters.

Lets say the bottles are labeled B1 through B32 and the 9 tasters are T1 through T9.

Let T1 taste from bottles B1 and B2, T2 from B3 and B4, T3 from B5 and B6, and so on.

Let T9 taste from the odd numbered bottles i.e. B1, B3, ...., B31.

One, and only one, of tasters T1 through T8 will die. Without loss of generality, suppose T1 died. This means one of the bottles B1 and B2 is poisoned. Now, if T9 died, then the poisoned bottle is T1, otherwise its T2. The key idea is that from T1 through T8 we narrow down the possibility to one out of two bottles, and T9 identifies which one of the two it is.

Can it be done better?

Rooju

[zuselegacy]

for the wine tasting problem, 5ppl r enough i guess. Its only based on combinations.
nobody drinks bottle 1, only 1 person drinks bottle 2 , person2 drinks bottle 3....
further, person 1 and 2 drink bottle 7 and so on. finally the combination that occurs willl be the poisoned bottle. in otther words, ceiling[(log 32)base 2]=5

[zuselegacy]

and for the buliding problem , strategy would be along the lines of binary search.
start on the 50 the floor, if it breaks,use the 25th floor or else use 75th floor.
after log nbase2 attempts ul get value of F

[zuselegacy]

for the beatles question, 1st Johan and paul cross and john returns. this adds to 2+1=3. now george and ringo cross . Paul whos waiting on the other side, takes the torchn and returns back. this adds to 10+2=12.now John and Paul join the others on the other side=2.
So in total, 3+12+2=17.

[Agilemind]

n a multiple choice ques having 4 options, one is awarded 1 mark for
correct and -x for wrong ans.
if one answers randomply and get 0 marks find value of x.
(ans is considered correct only when one ticks all the correct options)

x = 1/10 Assuming all combinations of answers possible and are picked from uniformly.
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3x = total = 9*r = 9x/cr Therefore cr = 3
r = # parrots = x/cr -> r = 10
p = # peacocks = x/cp -> cp = 30/28
d = # doves = r+5 = x/cd = x/3+5 ->x(1/2-1/3) = 5 -> x = 30, d=15
cr = cd+1 = 3 -> cd = 2
3x/cr = 2+p = x -> p=28

cr = 3, cd = 2, cp = 28/30
r = 10, d = 15, p = 28
x = 30
total money = 90

a man spends 3 equal sums of money in purchasing doves,parrots and
peacocks.A parrot cost 1 rs more that
a dove.Had the man invested all his money in parrots,he would have been
able to
buy 2 parrots more that the number of peacocks he had purschased
earlier.also the man purchased 5 more
doves than parrots. the total sum of money he spent on purchasing the
birds is equal to 9 times
the total number of parrots he purchased. find the number of doves,
parrots and peacocks
he purchased and total minimum amount of money he spent.
-----------------------------------------------------------------------------

there is a chain of trianges whose vertices are metal beads. if the
sides of triangles
are formed by joining a single thread to the metal beads what will be
the length of the thread reqd. to form the chain
of 6 triangles of unit sides using 13 beads.
3*6 = 18 units
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I am in a 100-story building. I have with me two glass balls. I know
that if I throw the ball out of the window it will
never break if the floor number is less than F and it will always
break if the floor number is equal or greater than F.
Assuming that I can reuse the glass ball which didn't break, what is
the minimum number of throws required to find F and
the strategy to find F?

Only go to every other floor starting at the second floor and working your way up if the ball breaks go down one floor and check. worst case senario 51 tries.
-------------------------------------------------------------------
One day two mathematicians, Igor and Pavel, meet in the street.
"I have three sons," says Pavel. "The product of their ages is equal to
36." Looking around and then
pointing to a nearby house, Pavel says, "The sum of their ages is
equal to the number of windows in the building over
there."
Igor thinks for a minute and then responds, "Listen, Pavel, I cannot
find the ages of your sons."
"Oh, I am very sorry", says Pavel; "I forgot to tell you that my
oldest son has red hair."
Now Igor is able to find the ages of the brothers. Can you do it?

x*y*z = 36 -> x,y,z = {(6,3,2),(6,6,1),(36,1,1),(12,3,1),(18,2,1),(9,2,2),(4,3,3)}
two of these add to the same sum : 9+2+2=13, 6+6+1=13 by knowing there is a singlular oldest with red hair it must be 9,2,2

[Agilemind]

Last number one:
His answers >500 yes (lie), square no (lie), cube yes (truth)
Reality <500, square, cube so number is 64

[Agilemind]

As for the tasting you can do it with 5 but probably more than one will die so having 31 tasters is most efficient death wise because less than 1 is expected to die. too lazy to work out how many you expect to die with 5 tasters but more than 1.