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        riddles >> easy >> Some Answers to Easy Section
        
(Message started by: TenaliRaman on Jun 2nd, 2003, 1:41am)
Title: Some Answers to Easy Section
Post by TenaliRaman on Jun 2nd, 2003, 1:41am
Marble Jars1->
[Hide]
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)
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Arab Sheikh Camels->
[Hide]
Switch Camels
Note that : the camel that finishes last wins the fortune for its owner.(the key sentence)
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3 Hats->
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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.
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Humming Bird

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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.
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FOOT SIZE IMPLIES SPELLING ABILITY

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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 :) )
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NONHOMOGENEOUS ROPE BURNING

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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.
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WILLYWUTANG AND THE BURNING ISLAND OF DOOM

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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.
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TWO COIN FLIPS

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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
[/Hide]
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 2nd, 2003, 1:50am
COIN MACHINE WEIGHING

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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)
[/Hide]

(Will Post a few more later)
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 2nd, 2003, 7:54am
HOURGLASSES

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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.
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LOGICAL SIGNS I

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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.
[/Hide]
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 2nd, 2003, 8:12am
LOGICAL SIGNS II

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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)
[/Hide]
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 2nd, 2003, 8:51am
CHESS PUZZLE I

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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 _ _ _ _ _ _

[/Hide]

CHESS PUZZLE II

[Hide]
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

[/Hide]
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 2nd, 2003, 9:51am
CORK, BOTTLE, COIN

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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)
[/Hide]

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

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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.
[/Hide]
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 2nd, 2003, 10:23am
STUPID

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The answer is "E".
No marks for guessing the reason for the title of this puzzle. :)
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CLIMBING SNAIL

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In 15 days it climbs 15 meters.In the 16th day it climbs the remaining 5 meters and that's it.
Answer : 16 days
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8-WAY CAKE SLICE

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Cut the cake into 4 equal parts.(This accounts for two slices).
Now make a cut along its height,to get 8 equal parts.
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CHESSBOARD SQUARE COUNT

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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
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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

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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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Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 2nd, 2003, 11:40am
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)
Title: Re: Some Answers to Easy Section
Post by THUDandBLUNDER on Jun 2nd, 2003, 11:51am
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?
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 2nd, 2003, 11:52am
TWO CONDOMS, THREE WOMEN

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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.
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PRIME PAIRS

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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
[/Hide]
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 2nd, 2003, 12:01pm
@ 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.
???
Title: Re: Some Answers to Easy Section
Post by THUDandBLUNDER on Jun 2nd, 2003, 12:15pm

Quote:
Humming Bird
i am not sure as to how your method works and why?

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  

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.

How far would they hang down?
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 2nd, 2003, 12:32pm
@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)
Title: Re: Some Answers to Easy Section
Post by THUDandBLUNDER on Jun 2nd, 2003, 2:50pm

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.

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)

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.  ;)
Title: Re: Some Answers to Easy Section
Post by Icarus on Jun 2nd, 2003, 5:40pm
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 (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1027805413) is the original "Logical Signs I" thread, in which you will find a full discussion of the problems with this puzzle.
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 3rd, 2003, 9:01am
@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?  


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).
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 3rd, 2003, 9:11am
@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  ;D )

I just checked that link you gave me.At the end of it all, i was left wondering who was right ???
Title: Re: Some Answers to Easy Section
Post by Icarus on Jun 3rd, 2003, 3:53pm
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.
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 4th, 2003, 8:05am
You are the boss and "[Hide]Boss is always right[/Hide]" ;)
Title: Re: Some Answers to Easy Section
Post by Chronos on Jun 4th, 2003, 10:56pm
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.
Title: Re: Some Answers to Easy Section
Post by THUDandBLUNDER on Jun 5th, 2003, 1:46am

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.

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!"
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 5th, 2003, 7:13am
@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"
--- [Hide] and i said it  ;D [/Hide]
Title: Re: Some Answers to Easy Section
Post by Icarus on Jun 5th, 2003, 5:00pm
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.)
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 6th, 2003, 11:02am

on 06/05/03 at 17:00:24, 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.)


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.
Title: Re: Some Answers to Easy Section
Post by Icarus on Jun 6th, 2003, 4:05pm
  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.
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 6th, 2003, 9:47pm
i suppose your co-workers are as qualified as you are.This becomes a barrier to accepting new information.Since they feel "i know as much as this guy does so why should i listen to him?" or it could be "i have been working like this and produced quality products,now why should i take risk and listen to this guy".

To deal with such type of people,the best way is way of Socrates "make them realise their mistake by asking them innocent looking question".

i am no psychological expert but this trick works when i have to convince my friends of my ideas.
Title: Re: Some Answers to Easy Section
Post by Chronos on Jun 11th, 2003, 1:54pm
Personally, I approach any problem with the assumption that it has a simple (if perhaps tricky) solution.  Most problems with difficult solutions are not worth asking in the first place.

Of course, this attitude just makes things harder for me when I do come across a genuinely difficult problem.
Title: Re: Some Answers to Easy Section
Post by fyo on Jun 25th, 2003, 8:46am
This is a bit of nitpicking regarding the answer to the Hour Glass puzzle...

TenaliRaman's suggestion was to:

1) Start both hour glasses.
2) When the 7min one runs out, "start the timer"
3) Let the 11min finish running out (4 mins).
4) Restart the 11min glass and you get 15 mins.

While correct, this is not the best way to do it. The problem is that you are limited in your ability to time the 45 minutes. If someone tells you tell him when 15 mins have past from NOW, you're dead in the water. The solution given requires (at minimum) a 7 minute head start.

The "proper" solution would be to:

TIMER STARTS NOW
1) Start both glasses.
2) When the 7min glass runs out, restart the 7min glass.
3) When the 11min glass runs out (the 7min glass has 3 minutes left), turn the 7min glass around. It will run out of sand after 4mins, giving the required 15mins total.
TIMER ENDS NOW

Sincerely,

fyo
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Jun 25th, 2003, 1:06pm
yes you are right
Title: final answer to Chess Problem I (long)
Post by Elysha on Aug 8th, 2003, 12:50am
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 _ _ _ _ _ _


This will not work, because neither the knight nor the bishop will be able to attack row 1 square 2.  I like the formatting you've used for the answer, though, so I'm going to use it to present the three possible answers I found.  There are no other answers possible, as I will show.

First I will label the positions we are filling from left to right, then top to bottom, as A, B, C, D, and E, like this:

A 1 _ _ _ 1 _ B
_ _ _ _ _ _ _ _
_ _ 0 _ _ _ _ _
_ _ _ _ 1 1 _ _
_ _ _ _ _ _ _ C
_ _ D _ _ _ _ _
_ _ _ _ _ _ _ _
_ E _ _ _ _ _ _

I will use these statements for further deductions: 1) Because of the 0, A cannot be the bishop or the queen.  2) D cannot be the rook or the queen.  3) B must be either the rook or the queen.

Only B, C, or E can be the queen.  I'm going to look at each of these possibilities in turn.

First, Suppose E is the Queen.  Then this is the only possible solution:

N 1 _ _ _ 1 _ R
_ _ _ _ _ _ _ _
_ _ 0 _ _ _ _ _
_ _ _ _ 1 1 _ _
_ _ _ _ _ _ _ K
_ _ B _ _ _ _ _
_ _ _ _ _ _ _ _
_ Q _ _ _ _ _ _

Here is my reasoning: Suppose E is a queen.

Then B is a rook. (see B)

Then D, in order to attack row 4, square 5, must be a bishop.

A is not a king, because row 1 square 2 can only be attacked by the queen in E.  A has to be a knight, the only possibility remaining to it.

If A is a knight, then the only position left to the king is C.

Now, let's suppose C is a queen.

If C is queen, then E must be the bishop, to threaten the position C fails to threaten.  In this case, there are no pieces left that can move horizontally.  Neither B nor D can threaten the position between them.  This is a contradiction, and it is not possible for C to be the queen.

Now, the third possibility: let's suppose B is the queen.  I found two possible solutions (similar to yours):

R 1 _ _ _ 1 _ Q
_ _ _ _ _ _ _ _
_ _ 0 _ _ _ _ _
_ _ _ _ 1 1 _ _
_ _ _ _ _ _ _ K
_ _ N _ _ _ _ _
_ _ _ _ _ _ _ _
_ B _ _ _ _ _ _

Also:

K 1 _ _ _ 1 _ Q
_ _ _ _ _ _ _ _
_ _ 0 _ _ _ _ _
_ _ _ _ 1 1 _ _
_ _ _ _ _ _ _ R
_ _ N _ _ _ _ _
_ _ _ _ _ _ _ _
_ B _ _ _ _ _ _

Reasoning:  Suppose B is the queen.  Then D is not the bishop, but is either the knight or the king.  Now, there are two possibilities: either E is not the bishop, or E is the bishop.  First, suppose E is not the bishop.

If E is not the bishop, then C is the knight.  

Now, D is not allowed to move diagonally because B is the queen.  D is also not allowed to move vertically, because it would threaten the position that isn't threatened by anything.  The only pieces left to D by this are knight and king.  Since C is the knight, D must be the king.

The only position left for the bishop to fill is A.  A is not allowed to be a bishop.  This is a contradiction.

Therefore, if B is the queen, E cannot be anything but a bishop.

Can E be a bishop?

Let's try that second case.  B is a queen; E is a bishop.

Then C is either a rook or a king, and A is either a rook or a king.  Since rook and king must be divided up someway between those two positions, the only position left to D is knight.  There are two possible scenarios: either the rook is in position C and the king is in D, or vice versa.

In sum, three possible scenarios and no others.
Title: Re: final answer to Chess Problem I
Post by wowbagger on Aug 8th, 2003, 4:21am
Elysha, you obviously invested a lot of time and effort. So sorry in advance for disproving your suggestions (or at least trying to do so).

I have the impression you misinterpreted the riddle. There are no other pieces on the board. "Green numbers indicate how many pieces could move to that square on the next move." This means that the square f8 (standard chess notation for top row, column 6) doesn't block the piece on h8 (top row, col. 8) from moving to b8 (top row, col. 2), for example.


on 08/08/03 at 00:50:38, Elysha wrote:
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 _ _ _ _ _ _


This will not work, because neither the knight nor the bishop will be able to attack row 1 square 2.

Actually, it does work. The queen attacks the square b8.


Quote:
First, Suppose E is the Queen.  Then this is the only possible solution:

N 1 _ _ _ 1 _ R
_ _ _ _ _ _ _ _
_ _ 0 _ _ _ _ _
_ _ _ _ 1 1 _ _
_ _ _ _ _ _ _ K
_ _ B _ _ _ _ _
_ _ _ _ _ _ _ _
_ Q _ _ _ _ _ _

Not valid, because b8 is attacked by queen and rook, so it would have to have a "2" instead of a "1".


Quote:
Now, the third possibility: let's suppose B is the queen.  I found two possible solutions (similar to yours):

R 1 _ _ _ 1 _ Q
_ _ _ _ _ _ _ _
_ _ 0 _ _ _ _ _
_ _ _ _ 1 1 _ _
_ _ _ _ _ _ _ K
_ _ N _ _ _ _ _
_ _ _ _ _ _ _ _
_ B _ _ _ _ _ _

Not valid, because b8 and f8 are attacked by queen and rook.


Quote:
Also:

K 1 _ _ _ 1 _ Q
_ _ _ _ _ _ _ _
_ _ 0 _ _ _ _ _
_ _ _ _ 1 1 _ _
_ _ _ _ _ _ _ R
_ _ N _ _ _ _ _
_ _ _ _ _ _ _ _
_ B _ _ _ _ _ _

Not valid, because b8 is attacked by king and queen.

By the way, the solution TenaliRaman gave for Chess Puzzle II is also correct.
Title: Re: Some Answers to Easy Section
Post by Elysha on Aug 8th, 2003, 3:46pm
Thanks a million!  Whyever didn't I see that?
Title: Re: Some Answers to Easy Section
Post by Elysha on Aug 8th, 2003, 4:14pm
Any moderator should feel to clear away my post if it's clogging things up.  It appears that I managed to post in the wrong thread anyway; I thought I had read some discussion of Chess Problem I in these pages, but I cannot find it anymore.
Title: Re: Some Answers to Easy Section
Post by wowbagger on Aug 8th, 2003, 4:34pm

on 08/08/03 at 16:14:59, Elysha wrote:
Any moderator should feel to clear away my post if it's clogging things up.  It appears that I managed to post in the wrong thread anyway; I thought I had read some discussion of Chess Problem I in these pages, but I cannot find it anymore.

Ha! The moderator who clears up all posts on this forum that are clogging things up hasn't been born yet!   ::)
But just in case he has and should happen to read this: Please start with the 0.999-thread. Oh, and have a particularly watchful eye for these duplicate threads.  ;D

And never mind posting to the wrong thread, this happens a lot to newbies. By the way, as a member, you can modify (and remove) your posts.
With regard to your wrong answers: This happens even to Überpuzzlers.  ;)
To quote a sig (sorry, I don't remember whose it is/was): "It is better to have puzzled and failed than never to have puzzled at all."
Title: Re: Some Answers to Easy Section
Post by Elysha on Aug 8th, 2003, 11:21pm
Ah!  But I wasn't registered yet when I posted.  Thank you for your kind words.  I'll be sticking around... these riddles are addictive.
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Aug 9th, 2003, 8:36am
The sig is of the UberPuzzler "Eric Yeh".
* This post is absolutely senseless but hey look out for my "post meter" it is inching towards 126 ;D *
Title: Re: Some Answers to Easy Section
Post by wowbagger on Aug 11th, 2003, 3:35am

on 08/09/03 at 08:36:29, TenaliRaman wrote:
* This post is absolutely senseless but hey look out for my "post meter" it is inching towards 126 ;D *

There are even more senseless posts...  ;)
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Aug 11th, 2003, 10:41am
LOL!!!!  :D  :D
Title: Re: Some Answers to Easy Section - foot Size and s
Post by Ziyaad on Aug 14th, 2003, 3:20am
The correlation is correct because, As a person gets older, their foot size generally becomes larger. Of course, as one gets older, one's spelling ability generally also improves!!!
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Aug 14th, 2003, 11:17am
yeap!! it seemed the only answer to me too ! But when i searched the forum for the answer i found some really goofy discussion on this (as usual).it may not be enlightening but certainly entertaining  ;) .
Title: Re: Some Answers to Easy Section: Marble Jar1
Post by jtrook on Sep 10th, 2003, 9:29am
Answer to Marble Jar.  I think from the reading of the question that each jar must have 50 marbles when you are finished.  It says redistribute (e.g. swap a black with a white).  The best probability is 50% if you don't swap any or if you even the jars with 25 black and 25 white.  I would prefer the second which leave the choice in your hands not random selection of the jar.
Title: Re: Some Answers to Easy Section
Post by aero_guy on Sep 10th, 2003, 12:24pm
jtrook, I won't spoil it for you, but there is a better solution (just shy of 75% survival).  There is a separate thread on the topic.
Title: Re: Some Answers to Easy Section
Post by jtrook on Sep 10th, 2003, 2:41pm
Thanks aero_guy,
I found the thread.  I wasn't considering the two jars events together.  I only looked at the 24.74% one jar and the 50% the other jar.
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Sep 10th, 2003, 4:12pm
*still feels he should have clicked "some others should,not this one*
::)
Title: Re: Some Answers to Easy Section
Post by Icarus on Sep 10th, 2003, 6:48pm
:D

It's nothing personal, TenaliRamen! I just think that they detract rather than advance the conversations, so I decided to see if this opinion was limited to me or if it was generally shared by those who have been around long enough to be aquainted with both single issue threads, and these in-mass ones. (Speaking of which, I'm restricting this to members only. Visitors who have been around that long really ought to register anyway! ;))
Title: Re: Some Answers to Easy Section
Post by otter on Sep 10th, 2003, 7:22pm

on 09/10/03 at 18:48:27, Icarus wrote:
:D

It's nothing personal, TenaliRamen! I just think that they detract rather than advance the conversations, so I decided to see if this opinion was limited to me or if it was generally shared by those who have been around long enough to be aquainted with both single issue threads, and these in-mass ones. (Speaking of which, I'm restricting this to members only. Visitors who have been around that long really ought to register anyway! ;))

I have to agree, Icarus.  I have come to view these "en-masse" responses as spoilers at best and "one-upsmanship" at worst.  One of the things that keeps me coming back to this forum is the great discussion and the thought that goes into the posts.  Many times I have learned much more from following the individual threads than I did from the riddle or puzzle itself.  As William notes, "how you get to the answer is more important that the answer itself".  
Title: Re: Some Answers to Easy Section
Post by mistysakura on Sep 11th, 2003, 2:13am
My reason for voting "some others should, not this one" is becuase I feel that the "easy" section doesn't generate much conversation after the puzzle is solved anyway, whereas in medium/hard/what happened etc, there ae usually many continuations after the initial "solving" of the puzzle.  some of them are extensions, and some are arguments against the answer.  I think that "easy" is much more clear-cut than most other categories, so there' not much harm done in leaving this one.  If these threads are kept in the harder forums though, it does lead away from the left-over conversation.
Title: Re: Some Answers to Easy Section
Post by TenaliRaman on Sep 11th, 2003, 8:08am
Icarus,
no probs!(which may slightly hint toward the fact that i share your viewpoint)
Title: Re: Some Answers to Easy Section
Post by Icarus_Bound on Sep 11th, 2003, 7:10pm
Some higher power must disagree, because as you can see by my lowly "guest" status, I am for some reason unable to log in. I've asked William, and he can find no problems at his end, and so far I have found nothing at mine.

So I guess your thread is safe from me until I can find a solution to a much more vexing puzzle!

Icarus
http://www.ocf.berkeley.edu/~wwu/YaBBImages/avatars/sylvester.gif
Title: Re: Some Answers to Easy Section
Post by towr on Sep 11th, 2003, 11:48pm

on 09/11/03 at 19:10:43, Icarus_Bound wrote:
Some higher power must disagree, because as you can see by my lowly "guest" status, I am for some reason unable to log in. I've asked William, and he can find no problems at his end, and so far I have found nothing at mine.
Have you tried logging in from a different computer?
Deleting all your cookies?
Having William change your password?
Title: Re: Some Answers to Easy Section
Post by Icarus on Sep 12th, 2003, 3:06pm

on 09/11/03 at 23:48:29, towr wrote:
Have you tried logging in from a different computer?
Deleting all your cookies?
Having William change your password?


Logging in from another computer works, and this one is through the same ISP account. Apparently the problem is in my machine. I have deleted all the cookies, cleared the cache, and turned the cache off. None of it made a difference. I may start reinstalling if nothing else works.
Title: Re: Some Answers to Easy Section
Post by SWF on Sep 15th, 2003, 10:14pm
There are some choices missing from the poll:

Delete this thread.

Put a copy of the text for each riddle mentioned in the header. This will make it is clear which problems people are being discussed. :)
Title: Re: Some Answers to Easy Section
Post by Icarus on Sep 16th, 2003, 3:42pm
I only delete threads that contain nothing of consequence - deleting this one would be unfair to those who have taken part in it. But locking it is another matter.

Putting the puzzle in the header - when it isn't given in the first post (a project I've started in the Hard forum, as you may have noticed) - is generally a good idea, but it doesn't really address my disatisfaction (and apparently others') with these threads. It is not so much the lack of puzzle statement, as it is the way they break up discussions, making them hard to follow, and the duplication of what is already contained in a different thread.

Another project - lock all but one thread for each puzzle. Even better would be to combine the duplicate threads, but this is not an ability that William has granted to us.
Title: Re: Some Answers to Easy Section
Post by THUDandBLUNDER on Sep 16th, 2003, 7:03pm
You could now delete: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1063599807
Title: Re: Some Answers to Easy Section
Post by SWF on Sep 16th, 2003, 9:12pm
Icarus, I was kidding about putting riddle statements in the header for this thread. Thus the :)

I would vote for deleting, but there are certainly enough votes to justify locking.

Since this thread is still accepting posts, I would like to add that I see 6 F's, the coin makes two revolutions, and the line will remain straight.
Title: Re: Some Answers to Easy Section
Post by Icarus on Sep 17th, 2003, 7:39pm
Since there is a conversation going on in this thread right now, I thought I would wait until it dies down before the actual locking. I ought to go lock the other catch-alls, but have too many things going on to do it right now.

In general, I don't like the idea of simply deleting posts. I don't see it as my job to throw past conversations out, even if they go astray. I just want to guide people to where the most effective use of their time is to be found. The only times when I would feel justified in deleting posts is when one of the conversants has already deleted their side, leaving the remaining posts make no sense - as occasionally happens when someone points out a problem in a new thread and the original poster deletes his post. Or if some complete idiot drops all pretense of civility (this would require far worse than the swelled head of the "Guest" in the 0.999... thread - but there are some lines that if crossed I would not hesitate to delete the post).
Title: Re: Some Answers to Easy Section
Post by wowbagger on Sep 18th, 2003, 12:46am

on 09/17/03 at 19:39:23, Icarus wrote:
Since there is a conversation going on in this thread right now, I thought I would wait until it dies down before the actual locking.

Seems like the perfect time to join in this conversation. ;)

I agree that threads like this one tend to get less and less clear the more riddles are being discussed. There is a sizable risk of discouraging newbies and especially first-time visitors by not directing them towards the focussed single-topic threads. However, even after locking this and similar threads, it is still possible that people wade through posts like this that do not deal with the riddle they are interested in because they did not find (or did not bother to search for) the "right" thread. Maybe the thread header could be used in a helpful way, even if only to point out the search feature to the readers one more time.
Title: Re: Some Answers to Easy Section
Post by Icarus on Sep 18th, 2003, 3:24pm
Sigh.... More work!  You're going to wear me out!

Actually that's a good idea - though I'll try to come up with something better later. Another idea might be to change the titles for the main threads for each puzzle in the easy section to exactly match the puzzle name. This would make it easier to seach out the correct thread.
Title: Re: Some Answers to Easy Section
Post by Bobbin on Jan 14th, 2005, 3:11am

on 06/02/03 at 10:23:09, TenaliRaman wrote:
GLASS HALF FULL

[Hide]
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.
[/Hide]
No, those conditions do not work, because water tends to "lip" in a glass. If you fill a glass to the top, you can invert the lip so that you're holding more water in the glass then the volume of the glass itself, and finally, if you freeze the water it becomes ice, which consumes more space then water - so if the water was frozen in the glass to begin with, you aren't going to be able to exercise that solution, and if you let it melt first, then it's taking up less space then it originally did and you still won't know if it's exactly half-full. Your answer is equally accurate to holding your hand over the edge and flipping the glass, really, which means IMHO there is no way to accurately determine if the glass is exactly half-full.
Title: Re: Some Answers to Easy Section
Post by Icarus on Jan 14th, 2005, 4:26pm
Alright - that's what I get for forgetting. Though few have expressed an opinion, a clear majority of those that have are in favor of the catch-all threads being shut down. So I am locking this thread. Bobbin, if you would like to discuss this, there is a thread devoted to the glass-half-full riddle (I think there is, anyway).


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