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TenaliRaman
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Some Answers to Easy Section
« on: Jun 2nd, 2003, 1:41am » |
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Marble Jars1->
Place 49 White Marbles from the original White Jar to the Black Jar.
Then if the White Jar is given , the chances that u live is 100%.
Then if the Black Jar is given , the chances that u live is 49*100/99 i.e 49.49% (which is well enough)
Arab Sheikh Camels->
Switch Camels
Note that : the camel that finishes last wins the fortune for its owner.(the key sentence)
3 Hats->
When A is asked the question,possible combination of hat colours on (B,C) are (Black,Black),(Black,White),(White,Black) and (White,White).
Note that A can correctly determine the colour of his hat only if (B,C)=(White,White)
But A answers "no" which means (B,C) must have one of the previous three combinations.
When B is asked the question,
he knows that (B,C) = (Black,Black),(Black,White) or(White,Black) .. (due to A's answer)
If C is White then from the above combination it is quite obvious that B has to be Black but If C is Black then B cannot determine his hat colour.
Now B says "no".So C knows that his hat colour must be Black.
Humming Bird
The calculations get a bit too tedious.
denoting d as the distance between LA and NY trains intially.
1st iteration
let bird travel a distance x and in the same time NY train travels d-x.
x/25 = (d-x)/20
Bird travels (5d/9)
NY train travels (4d/9)
LA train travels 15 * (5d/9)/25 = d/3
new distance between (LA-NY) = d-(d/3)-(4d/9) = (2d/9)
Similar such iterations (several of them) have to be made to get the answer.
I think writing a computer program to evaluate is feasible if time is at hand.
FOOT SIZE IMPLIES SPELLING ABILITY
Does this make sense?(i don't think so)
Anyways,
Age:Height Ratio is considered as a factor in the calculation of IQ,so i guess the correlation is a "direct implication".
(i hope the above makes sense  )
NONHOMOGENEOUS ROPE BURNING
Burn first rope on both ends and burn second rope on one end.
When the first rope completely burns out,it indicates completion of 30 minutes.
As soon as the first rope burns out,burn the second end of the second rope.When the second rope burns out,it would indicate the completion of 45 minutes.
WILLYWUTANG AND THE BURNING ISLAND OF DOOM
Start fire in some part between A and B.Its quite easy to calculate a safe distance considering the extrema conditions.
Logic is once the last part of the forest gets burnt out bcos of the fire started by willy,then willy can move to the already burnt part of the forest and save himself.
TWO COIN FLIPS
Two coins are flipped so
INITIAL SAMPLE SET : HH,HT,TH,TT
Atleast one is head so
REDUCED SAMPLE SET : HH,HT,TH
Probability = 1/3
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #1 on: Jun 2nd, 2003, 1:50am » |
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COIN MACHINE WEIGHING
Label the machines from 1 through 20.
From 1st machine take 1,From 2nd take 2 and so on.
total number of coins = 20*21/2 = 210
therefore if x is the weight of each coin.
Then total weight of 20 coins should ideally be = 210*x.
Suppose after weighing we get the weight as W.
Then the defective machine is given by,
defective machine = 210x - W
(ofcourse this is because coin in defective machine is one ounce less)
(Will Post a few more later)
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #2 on: Jun 2nd, 2003, 7:54am » |
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HOURGLASSES
Tilt both the hourglasses.As soon as the 7 minutes hourglass is over,that would mean that 4 minutes are left in the 11 minutes hourglass.We start our counter at this point.As soon as 11 minute hourglass finishes,tilt it again and wait for it to finish.Thus we have 11+4=15 minutes.
LOGICAL SIGNS I
This problem has occupied my mind for some three hours now and i cannot still come to a answer.It seems that the question has an answer but yet deceptive.
BTB,
Suppose that the inscription on the gold chest is true,then it is the chest that has true inscriptions.The inscriptions on the silver chest is false meaning that the python is in the gold chest and silver chest has the treasure.
Suppose that the inscription on the gold chest is false,then either both the inscription are true or both are false.Both cannot be true,since we have assumed that gold chest is false.If both are false,then again the inscriptions on the silver chest is false which implies that silver chest has the treasure.
Now,we have the answer that silver chest has the treasure.But the inscriptions that were written were arbitrarily chosen by ancient people.So it is possible that they have kept python in the silver chest and deliberately made those inscriptions.So the gold chest may have the treasure.
So now what to do ......
Option 1 : Flip a coin to find which chest to open.
Option 2 : Find a simpleton to open a chest for you.
Option 3 : Forget the treasure,life is worth more.
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #3 on: Jun 2nd, 2003, 8:12am » |
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LOGICAL SIGNS II
This one is a lot simpler that logical 1 since it is mentioned that the reader is aware that one inscription is true and one is false.
BTB,
Make a table....
1 - indicates true
0 - indicates false
U - indicates unsure
so possible cases,
S G B
1 0 U
0 1 U
U 1 0
U 0 1
1 U 0
0 U 1
Now simply wherever there is U put 1 and 0, and see what the statement imply (lot of contradictions will be achieved but finally the answer would be to open bronze chest)
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #4 on: Jun 2nd, 2003, 8:51am » |
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CHESS PUZZLE I
key to the solution .. (look at the 1's and check out the blue squares which target them)
In this puzzle the first row was important.Two blue squares where attacking that row and two places were marked with 1.Now there are 3 pieces which have horizontal movement King,Rook and Queen.King is certainly out of question (See the positions of the 1's).So it has to be the Rook or Queen.From here onwards its simply trial and error.
Finally we will have a solution which should look like this,
N-knight K-king Q-queen B-bishop R-rook
N 1 _ _ _ 1 _ Q
_ _ _ _ _ _ _ _
_ _ 0 _ _ _ _ _
_ _ _ _ 1 1 _ _
_ _ _ _ _ _ _ R
_ _ K _ _ _ _ _
_ _ _ _ _ _ _ _
_ B _ _ _ _ _ _
CHESS PUZZLE II
Again similar logic as to the first one.
In this puzzle,look at the 1 in the top left corner.Its attacked by two blue squares.The blue square on the third row can have a bishop or a queen.The blue square on the first row can have a queen or rook.Again from here,it is simple trial and error.(don't worry it doesn't take time at all).
The solution that one gets is,
1 _ _ _ _ K _ _
_ _ _ _ _ _ _ _
_ _ Q _ _ _ _ _
_ _ _ _ _ _ 1 _
_ _ _ 0 _ B _ _
0 _ _ _ _ _ _ _
_ _ 1 _ _ _ _ _
_ _ _ N _ _ _ R
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #5 on: Jun 2nd, 2003, 9:51am » |
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CORK, BOTTLE, COIN
The old favourite puzzle.
Answer : Hey i cannot take out the cork,so why don't i simply push it inside.
An interesting answer by my friend : Hey nothing was mentioned as to which bottle was corked and in which the coin was kept (meaning both the bottles need not be the same).So simply tilt the bottle containing the coin and it should come out.
(I am not sure if this is a proper answer,but,i find nothing to make this invalid)
The other three puzzles-->
FAMILY RELATIONS
ANALOG CLOCK I
ANALOG CLOCK II
are quite simple.So nothing required to explain as such here.
APPLES AND ORANGES
key sentence : You know that the labels are currently misarranged, such that no box is correctly labeled.
You have three choices
1>pull a fruit from the box labelled apple
2>pull a fruit from the box labelled oranges
3>pull a fruit from the box labelled apple and oranges
Consider first choice,
case 1 : You pull out a apple.
Since the box is labelled wrongly,it cannot be the apple box.Hence it has to be the "apple and orange" box.The other two labels are simply swapped.
case 2 : You pull out a orange.
Cannot determine anything.
Consider second choice,
case 1 : You pull out a orange.
Since the box is labelled wrongly,it cannot be the orange box.Hence it has to be the "apple and orange" box.The other two labels are simply swapped.
case 2 : You pull out a apple.
Cannot determine anything.
Consider third choice,
case 1 : You pull out a apple.
Since the box is labelled wrongly,it cannot be the "apple and orange" box.Hence it has to be the "apple" box.The other two labels are simply swapped.
case 2 : You pull out a orange.
Since the box is labelled wrongly,it cannot be the "apple and orange" box.Hence it has to be the "orange" box.The other two labels are simply swapped.
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #6 on: Jun 2nd, 2003, 10:23am » |
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STUPID
The answer is "E".
No marks for guessing the reason for the title of this puzzle.
CLIMBING SNAIL
In 15 days it climbs 15 meters.In the 16th day it climbs the remaining 5 meters and that's it.
Answer : 16 days
8-WAY CAKE SLICE
Cut the cake into 4 equal parts.(This accounts for two slices).
Now make a cut along its height,to get 8 equal parts.
CHESSBOARD SQUARE COUNT
Sum( i=1 to 8 ) i^2 = (8 * 9 * 17)/6 = 204
Sidenote : Sum( i=1 to n )i^2 = [n(n+1)(2n+1)]/6
MONTY HALL SHOW
This is quite a famous puzzle.So there is no need to describe it here as lots of info can be obtained on net about this.One can check mathforum.org for a good answer.
GLASS HALF FULL
Consider the front view or the side view of the cylinder.What is it??Its nothing but a rectangle.
You know that the diagonal bisects a rectangle.So simply tilt the glass and see if the surface forms the diagonal.
An easy condition check can be derived from this for more than half and less than half determination.
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #7 on: Jun 2nd, 2003, 11:40am » |
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HANGING CHAIN
(i am not very confident with this answer, so please someone do cross-check it if possible) (thanking in advance)
The shape assumed by a flexible chain ,which is supported at its ends and is acted upon by a uniform gravitational force, is called a catenary.
its equation can be parameterised as,
x(t) = t
y(t) = a*cosh(t/a)
its arclength is given by ,
s(t) = a*sinh(t/a)
Now this a is to be obtained first given the fact that we have the length of chain.
i got a=1/6 (cross check this please!!)
and the final answer as,
(1/3)*arccosh(19)
(again please do cross check this)
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ThudnBlunder
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Re: Some Answers to Easy Section
« Reply #8 on: Jun 2nd, 2003, 11:51am » |
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HUMMINGBIRD:
You are doing it the hard way.
Simply divide the distance from LA to NY by relative speed of trains and multiply by bird's speed.
LOGICAL SIGNS I:
This statement is not true. Therefore...
HANGING CHAIN:
If you cut the chain in half, what would happen?
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #9 on: Jun 2nd, 2003, 11:52am » |
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TWO CONDOMS, THREE WOMEN
For First Woman,
Put on both the condoms
For second,
Remove the top condom
For the third,
Take the condom which was removed earlier,turn it inside out and put in on again.
PRIME PAIRS
Consider a prime pair "p" and "p+2"
Now we know that product of three consecutive numbers is divisible by 3.
[Note : In general product of n consecutive numbers is divisible by n.This can be easily proved by pigeonhole principle]
therefore, p*(p+1)*(p+2) is divisible by 3.
p and p+2 are primes hence (p+1) is divisible by 3.
all primes greater than 2 are odd.Therefore,p and p+2 are odd.Therefore p+1 must be even and hence divisible by 2.
p+1 is divisible by 3 and 2.Also gcd(3,2)=1.Hence p+1 is divisible by 6. QED
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #10 on: Jun 2nd, 2003, 12:01pm » |
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@ Thud and Blunder
Humming Bird
i am not sure as to how your method works and why?
Logical Sign 1
Err!! I am not getting your point 
Hanging Chains
well if it were cut in half,the chain would split up and we would get two vertical chains hanging from respective tacks.
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ThudnBlunder
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Re: Some Answers to Easy Section
« Reply #11 on: Jun 2nd, 2003, 12:15pm » |
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Quote:Humming Bird
i am not sure as to how your method works and why?
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Distance travelled by bird = speed X time.
We know its speed. For long is it flying?
Quote:Logical Sign 1
Err!! I am not getting your point
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Not True does not necessarily imply False. Could be Undecidable.
Quote:Hanging Chains
well if it were cut in half,the chain would split up and we would get two vertical chains hanging from respective tacks.
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How far would they hang down?
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #12 on: Jun 2nd, 2003, 12:32pm » |
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@Thud and Blunder
Humming Bird
I see it your way
time taken = 5000/35 hrs
distance travelled by bird = 25 * 5000/35 = 3571.43 miles
Logical Sign 1
In mathematical logic,a proposition has one of two values either true or false.So if a proposition is not true,it implies false.
Hanging Chain
it will hang down by 3m.
(wouldn't this mean that distance between tacks is zero that is they are very close to each other)
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Re: Some Answers to Easy Section
« Reply #13 on: Jun 2nd, 2003, 2:50pm » |
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Quote:Logical Sign 1
In mathematical logic,a proposition has one of two values either true or false.So if a proposition is not true,it implies false. |
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Possibly not, if a statement refers to itself.
In Logical Signs I, the Gold Chest inscription says "One of these two inscriptions is true."
So it is indirectly saying something about its own truth value, eg, if one Chest said "The other inscription is true" and the other Chest said "The other inscription is false", which one is true and which one is false?
Quote:| (wouldn't this mean that distance between tacks is zero that is they are very close to each other) |
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Yes, it is a trick question. 
-----------------------------------------------------------------------
Rather than re-invent the wheel, why not read the relevant threads first?
But only after you have solved the puzzles, of course. 
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| « Last Edit: Jun 2nd, 2003, 3:04pm by ThudnBlunder » |
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Icarus
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Re: Some Answers to Easy Section
« Reply #14 on: Jun 2nd, 2003, 5:40pm » |
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TenaliRamen: If you look through the forums you will find threads (often multiple threads) for all of these puzzles. The "Search" tool on the toolbar at the top of your screen can be very useful. These "answers to everything" threads are really not a good idea. You are missing out on the discussion that has already taken place, and it makes it hard to track any new discussions, as you have to sort through the discussion of the other puzzles.
For instance here is the original "Logical Signs I" thread, in which you will find a full discussion of the problems with this puzzle.
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #15 on: Jun 3rd, 2003, 9:01am » |
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@Thud and Blunder
Quote:
Possibly not, if a statement refers to itself.
In Logical Signs I, the Gold Chest inscription says "One of these two inscriptions is true."
So it is indirectly saying something about its own truth value, eg, if one Chest said "The other inscription is true" and the other Chest said "The other inscription is false", which one is true and which one is false?
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I think i get what you mean.I think you mean to say , there is no way of determining the truth value if the statement becomes a paradox (which in this puzzle is quite possible).
If we were to consider that case,i don't think there is a way of determining which chest to open though i maybe wrong.What is the answer then
Hanging Chains
Ok i was totally fooled in by the question
I should have got the answer even through the catenary equation though  (Blame my poor calculation skills for that).
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #16 on: Jun 3rd, 2003, 9:11am » |
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@Icarus
I am really quite sorry as i didn't realise the interference created by my answers.(Though i kept them hidden so that only those who want to see the answers may see it).
I did not surf through the entire site and actually never saw the search button for a start.I thought rather than wade through a huge list of posts,i rather start one of my own.(As a student of comp engg., i always had "programming efficiency" as my top priority positively implying that i am quite lazy  )
I just checked that link you gave me.At the end of it all, i was left wondering who was right
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Icarus
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Re: Some Answers to Easy Section
« Reply #17 on: Jun 3rd, 2003, 3:53pm » |
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Well - that should be obvious! I'm right - always! You just remember that!!
Seriously: Here are salient points:- There is nothing guaranteeing that the signs have anything to do with the contents. They may give clues, or they may be misleading.
- Assuming that the signs are actual clues to the contents, There is still nothing to guarantee that either is true or false. As T&B has said, they could be undecidable.
- It is easy to mess up when you approach a logical problem as you did above, by assuming some statements are true and others false, and seeing what the consequences are. A far better approach is to examine the various possible cases being described and figuring out truth and falsity from them. For this situation, it looks like this:
Treasure in Silver, Python in Gold: Silver = false; Gold is undecidable (true => true & false => false)
Python in Silver, Treasure in Gold: Silver = true; Gold is true or contradictory depending on how you interpret it:
"One" means "at least one": Gold = true
"One" means "exactly one": Gold is contradictory (true => false & false =>true)
However, since there is nothing to indicate what set of truth values for the signs corresponds to the correct answer, this gains you nothing. That is why the puzzle has no solution as it is stated. Finding an unsuspecting victim to open the chests is your best hope for opening them.
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #18 on: Jun 4th, 2003, 8:05am » |
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You are the boss and "Boss is always right"
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Chronos
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Re: Some Answers to Easy Section
« Reply #19 on: Jun 4th, 2003, 10:56pm » |
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You also picked the harder way to solve Logical Signs II. Rather than listing all the possibilities of true/false for the signs (at least 6), it's easier to list the three possibilities for where the treasure is.
It's somewhat amusing, by the way, that the last time someone tried a sweep of the easy section, he did the hummingbird problem the hard way, too.
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Re: Some Answers to Easy Section
« Reply #20 on: Jun 5th, 2003, 1:46am » |
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Quote:| It's somewhat amusing, by the way, that the last time someone tried a sweep of the easy section, he did the hummingbird problem the hard way, too. |
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I remember reading an apocryphal (?) story about when von Neumann was given this puzzle. After a couple of seconds thought he gave the correct answer. When teased by his colleagues that they thought he might try to sum the infinite series, he replied "I did!"
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| « Last Edit: Jun 5th, 2003, 3:05am by ThudnBlunder » |
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Re: Some Answers to Easy Section
« Reply #21 on: Jun 5th, 2003, 7:13am » |
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@chronos
Neat idea for Logical Signs II.
As for my method for Humming Bird,it is said that "hard ways are easily seen but the easier ones comes by experience"
--- and i said it
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Icarus
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Re: Some Answers to Easy Section
« Reply #22 on: Jun 5th, 2003, 5:00pm » |
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Would that it were true, but the fact is those with lots of experience tend to pull out the most powerful tools first, forgetting to see if something easier is possible. Those who know only algebra find the hummingbird problem easier than those aquainted with calculus, because it never occurs to the former to try and sum up an infinite series! Thus the story about Von Neumann. (I recall hearing this story before, but I think it was told of a different mathematician - the story may have been corrupted with time.)
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TenaliRaman
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Re: Some Answers to Easy Section
« Reply #23 on: Jun 6th, 2003, 11:02am » |
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on Jun 5th, 2003, 5:00pm, Icarus wrote:| Would that it were true, but the fact is those with lots of experience tend to pull out the most powerful tools first, forgetting to see if something easier is possible. Those who know only algebra find the hummingbird problem easier than those aquainted with calculus, because it never occurs to the former to try and sum up an infinite series! Thus the story about Von Neumann. (I recall hearing this story before, but I think it was told of a different mathematician - the story may have been corrupted with time.) |
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Though i agree with you partially but i have one argument,Experience should actually teach one "what to use when".(That is why Field Experience is as important as the Bookish Knowledge.)If a person is unable to learn from experience,he is probably incapable of self-development.
But then mistakes do happen.(After all we are all humans.)So there may be times when a intelligent person gets a bit out of track.
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Re: Some Answers to Easy Section
« Reply #24 on: Jun 6th, 2003, 4:05pm » |
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I also agree partially. Experience does teach you what works and what doesn't (if you actually learn from it - more rare than people would have you think), but it can also put blinders on you as to what else is possible.
When I started my current job three years ago, it did not take me long to become appalled at the labor intensive, error prone procedures being used by my group. I have been working to change those procedures, with others who are equally appalled, but many in the group don't even understand the need. "It's worked for me so far" is the point-of-view they have, failing to realize how much better it could be.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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