# 7 problem solving questions. Help me answer it.



## mkerala (Feb 21, 2012)

In the following problems, Θ = 20 + units digit of your day of birth. For example, if you
were born on April 1st, then Θ = 20 + 1 = 21. If you were born on March 30th, then Θ = 20
+ 0 = 20. 

1. Alok and Bhanu play the following game on arithmetic expressions. Given the
expression
N = (Θ + A)/B + (Θ + C + D)/E
where A, B, C, D and E are variables representing digits (0 to 9), Alok would like to
maximize N while Bhanu would like to minimize it. Towards this end, they take turns in
instantiating the variables. Alok starts and, at each move, proposes a value (digit 0-9)
and Bhanu substitutes the value for a variable of her choice. Assuming both play to their
optimal strategies, what is the value of N at the end of the game? Also find a sequence
of moves (digits by Alok and variables by Bhanu) that would yield this value.
Note: Moves that lead to a divide-by-zero condition are disallowed. A non-optimal
sequence of moves is (5 → B, 6 → C , 3 → D, 2 → E, 0 → A) and the expression
evaluates to Θ/5 + (Θ+9)/2.

2. The mean, unique mode, median and range of 21 positive integers is 21. What is the
largest value that can be in this sequence? Also find such a sequence.
Note: Given a sequence of numbers a(1) ≤ a(2) ≤ ... ≤ a(n),
 The median of the sequence is the middlemost value in the sequence if n is
odd and the average of the two middle values if n is even.
 The mode is the most occurring value in the sequence
 The range is the difference between the largest and the smallest values, i.e.
a(n) - a(1).
For example, the sequence 2, 3, 4, 6, 6, 9 has mean = (2 + 3 + 4 + 6 + 6 + 9)/6 = 5,
median = (4+6)/2 =5, mode = 6, and range = 9 – 2 = 7.

3. A secret message is divided into Θ parts and each part is shared with a different
person. People communicate with each other using two-way phone calls and, in each
communication, share all the information they know until that point. What is the minimum
number of communications required for all Θ of them to know the secret? Find a
sequence of communications that achieves this minimum.

4. An equilateral triangle ABC with sides of length Θ cm is placed inside a square AXYZ
with sides of length 2*Θ cm so that side AB of triangle is along the base of the square
(as shown). The triangle is rotated clockwise about B, then C and so on along the sides
of the square until the points A, B and C return to their original positions. Find the length
of the path (in cm) traversed by point C.

*www.flgoo.com/downloads/image3.png

5. A bag contains printed articles of 4 different kinds: periodicals, novels, newspapers
and hardcovers. When 4 articles are drawn from the bag without replacement, the
following events are equally likely:
 the selection of 4 periodicals
 the selection of 1 novel and 3 periodicals
 the selection of 1 newspaper, 1 novel and 2 periodicals and
 the selection of 1 article of each kind
What is the smallest number of articles in the bag satisfying these conditions? How
many of these are of each kind?

6. Given a 9 x Θ chessboard, a rook is placed at the lower left corner. Players A and B
take turns moving the rook. A plays first and each turn consists of moving the rook
horizontally to the right or vertically above. The last person to make a move wins the
game. At the completion of the game, the rook will be at the top right corner. For
example, the figure below shows a 3 x 4 chessboard and the sequence of moves that
leads to a win for player A.
Does player A have a winning strategy in the given 9 x Θ chessboard? If so, what is the
strategy? If not, what is player B's winning strategy?

*www.flgoo.com/downloads/image4.png

7. A spaceship on an inter-galactic tour has to transfer some cargo from a base camp to
a station 100 light sec away through an asteroid belt. The ship can carry a maximum of
100 kgs of cargo and, as a result of colliding against the asteroids, every 2 light sec of
travel causes it to lose 1 kg of cargo. There are 300 kgs of cargo available at the base
camp. Find the maximum amount of cargo (in kg) that the ship can transfer to the
station? Assume that the spaceship can store the cargo at any intermediate point along
the way and that stored cargo is not depleted by the asteroids.
Prerequisites

Please answer as many questions as you can.


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## eggman (Feb 22, 2012)

Wow!! My mind just melted!!


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## tkin (Feb 22, 2012)

I'll make up as I go along:

No 3. (Θ-1)^Θ

Expl: There are Θ people, each having one part of a message, now, he needs to broadcast this to (Θ-1) people, this task is done by all Θ people.

PS: If by two end calls you mean simultaneously, then (Θ-1)+(Θ-2)....3+2+1
(Expl for this: Say 5 people, one guy makes phone call to all, he now know everything, so only (5-1) people left to share secret(each knows 2 parts now), now another guys makes call, he needs to call (4-1) people, he now knows all, like this)

For no 4. C moves in a circular path, assuming this, I guess 3/2*(pie*Θ), I still need to work on this, *this is probably wrong.*

Exp: Need to draw figures as we go along, equi triangle, so 60deg internal angle, do the rest.



mkerala said:


> In the following problems, Θ = 20 + units digit of your day of birth. For example, if you
> were born on April 1st, then Θ = 20 + 1 = 21. If you were born on March 30th, then Θ = 20
> + 0 = 20.
> 
> ...


What the hell does that even mean? 

I'll try to answer a few more, but you ruined my breakfast.


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## pramudit (Feb 23, 2012)

mind blowing questions... read question quater part and then thought what the hell is this and left it....


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## tkin (Feb 23, 2012)

I am pulling me hairs off trying to solve these.


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## whitestar_999 (Feb 23, 2012)

Prob.5:took about 10 min because my maths is not good but i find probability/permutation combination the easiest topic.might be wrong but still this is what i got:
4 periodicals,1 novel,2 newspapers,3 hardcovers.
someone with a good understanding of maths/fractions should be able to do it in 5 minutes.


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## Zangetsu (Feb 23, 2012)

@OP: are these IIT exams questions?


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## tkin (Feb 23, 2012)

Zangetsu said:


> @OP: are these IIT exams questions?


No way in hell.


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## whitestar_999 (Feb 23, 2012)

probability problem is too easy for IIT JEE of my time but not sure as i am not in touch with current level of JEE.

Prob.6:
for my case board was 9*22 & this is what i got:B can only win for sure in 1 scenario if A in 1st move place R in 2nd last column.in all other scenarios A will win unless he made a critically wrong move.


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## tkin (Feb 24, 2012)

I am too tired, can we get the answers already?


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## Niilesh (Feb 29, 2012)

Q.4
9√3Θ + 9Θ/2 or 9Θ(√3 + 1/2)


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## tkin (Feb 29, 2012)

OP Doesn't reply to thread:

*images.icanhascheezburger.com/completestore/2008/2/5/whywontthis128467435222991026.jpg


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## Niilesh (Feb 29, 2012)

Q.3
(Θ-1)/2 * (Θ)


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## mkerala (Mar 13, 2012)

1. didnt understand the question properly 


2. 7, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 28, 28.


3. (Θ-1) times for the first person to know everything. as he communicates with the last person he also tells everything he knows to that person so the remaining (Θ-2) people should call once atleast to know everything which adds upto --- (Θ-1)+(Θ-2)


4. while moving around a fixed point the side will become the radius for the arc. it takes three rounds for c to come tothe original position and on calculating the whole thing it comes to 2*22/7*Θ*10/3


5. a minimum of 7 articles total. 4-periodicals, 1-novel, 1-newspaper, 1-hardcover


6. player A can win easily as Θ > 20. he has to make sure that he moves to the right end in more than 9 steps


7. 150kgs (i assumed empty ship has no wt loss) 


Are these answer correct?


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