# A Riddle Using Deductive Reasoning

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### #1 Schera Do

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Posted 08 November 2015 - 06:36 AM

[I want to confine my discussion to "x + y" in the source thread of this riddle.]

...
You have 5 bottles on a table from left to right. One of them has poison in, you have to find out which one. I will number each object from left to right, from 1 to 5 like in this picture;

bottles.jpg

You deduce which number bottle it is from the following information;

- The poison is in a round bottle that is small.
- The bottles at each end of the table are large bottles, and there are no other large bottles on the table.
- There is a large bottle next to the poisoned bottle.
- One bottle is a cylindrical shape
- Bottle number 2 is not cylindrically shaped
- The poisoned bottle is not next to a cylindrically shaped bottle

Which bottle number is the poison?

(this is not really aimed at you Schera, but at anyone who wants to have a go at solving the riddle using deductive reasoning.)

.

Okay, I can't resist giving the answer, it is in the text below this sentence, you have to highlight the text, I made it invisible in case people still want to figure it out without knowing the answer:

It can't be bottles 1 or 5 as they are large bottles, and the bottle of poison is a small round bottle. It can't be bottle 3 because the bottle of poison is next to a large bottle. So the bottle of poison can only be either bottle 2 or 4. Since bottle 2 can't be a cylindrical bottle and the bottle of poison is not next to a cylindrical bottle then the bottle of poison must be bottle 2 because if it was bottle 4 then the cylindrical bottle would have to be next to it since bottle 2 is not cylindrical, and it was stated that the bottle of poison does not have a cylindrical bottle next to it.

.
(I have yet to view the answer.) If you had specified that the poison is in liquid form, then I would have choosen the one that isn't empty as you haven't specified that the others contain anything.

### #2 GodlessGamer

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Posted 08 November 2015 - 04:45 PM

It doesn't seem you've provided enough information. We know 1 and 5 are large since the bottles at each end are large, while the middle three are small. So the small, round poison bottle is 2, 3, or 4. The poison is next to a large bottle, so that rules out 3. At least one of the five is cylindrical, which isn't 2, and isn't next to the poison. That seems to be a red herring since the rest of the bottles could be cylindrical, spherical, cubical or even pyramid-shaped for all we know. The poison could be a cylindrical 4 (with no cylindrical next to it), or a spherical 2 (with the cylindrical in 4 or 5), or it could be a spherical 4 (with no cylindrical next to it), but I don't see how to deduce it from the clues given.

### #3 Goku

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Posted 08 November 2015 - 07:06 PM

It doesn't seem you've provided enough information. We know 1 and 5 are large since the bottles at each end are large, while the middle three are small. So the small, round poison bottle is 2, 3, or 4. The poison is next to a large bottle, so that rules out 3. At least one of the five is cylindrical, which isn't 2, and isn't next to the poison. That seems to be a red herring since the rest of the bottles could be cylindrical, spherical, cubical or even pyramid-shaped for all we know. The poison could be a cylindrical 4 (with no cylindrical next to it), or a spherical 2 (with the cylindrical in 4 or 5), or it could be a spherical 4 (with no cylindrical next to it), but I don't see how to deduce it from the clues given.

With the information given I say it is impossible to tell since the cylindrical bottle could be any bottle except 2. If 1 is cylindrical then bottle 4 is poisoned. If 3 is cylindrical then none of them have poison. If 4 or 5 is cylindrical then 2 is poisoned.

I cheated and looked at the answer and the cylindrical bottle is not a red herring, but I think the hint is more ambiguous than intended which makes it impossible to solve. I will say that we can assume there really is a bottle of poison on the table as a verified axiom. It is not a trick problem, and IMHO trivially easy once you correctly decipher the cylindrical hint which is why I won't say what I think it means.

### #4 mike the wiz

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Posted 09 November 2015 - 04:57 AM

Goku: I cheated and looked at the answer and the cylindrical bottle is not a red herring, but I think the hint is more ambiguous than intended which makes it impossible to solve

No you haven't understood that it is possible to be solved. I shall explain more below, highlight the text to read it;

Number 1 and 5 are large bottles, so the poison can't be in them.

That means you have bottles 2,3, and 4 left as possibilities.

The puzzle states that the bottle with poison in it is next to a large bottle, so if the poison was bottle number 3, then it could not be next to a large bottle because only bottle 1 and 5 are large. This means the poison can only be in either bottle 2 or 4. That is what you have to concentrate on - that now we know it can only be 2 or 4.

The puzzle states that bottle 2 is not a cylindrical bottle and that the poisoned bottle is NOT next to a cylindrical bottle.

So there are two bottles left.

So then if we assume the bottle of poison was number 4, then the cylindrical bottle could not be bottle 3 because the bottle of poison is "not next to a cylindrical bottle" according to the puzzle, but the cylindrical bottle could also not be in position 2 because the puzzle states that "bottle 2 is not cylindrical".

Therefore the poison MUST be bottle 2 because then you can put the cylindrical bottle in position 4, to satisfy all of the facts.

The problem isn't with the creator of the Goku.

### #5 mike the wiz

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Posted 09 November 2015 - 05:01 AM

Schera, thanks for posting it.

These puzzles can be tricky because of our human nature. We tend to complicate things. I myself would also struggle to get this, I think I failed to come up with the correct answer for J.K.rowlings puzzle because like you guys, I created complications the puzzle didn't ask me to create.

I think you should keep trying before peeking - it can be solved using the information provided. You just have to DEDUCE - but deducing isn't always easy. If my job was to make it easy I would have given the following deductive-puzzle.

Who is in the bathroom-puzzle.

Three people are in the house. Bob, Rob and Pob.

Pob is in the living room. Rob is in the kitchen.

Who is in the bathroom if someone is in there?

(that's an A,B,C level that presents a limited-choice that can be deduced by eliminating the two other, "or"s

EXAMPLE:

I love my pet. But I am not a dog person. I am not a cat person.

Find out which animal I love. In this example, deductive-reason can't be used because it is open-ended, - we could only deduce the answer if there were three possible pets on earth. However we could use inductive-reasoning to make a decision based on statistical probability, and we could ARGUE from our induction of evidence, that it is probably a rabbit, if our statistics show that the rabbit is the third most popular pet to have.)

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### #6 thatsneakyguy

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Posted 09 November 2015 - 05:51 AM

[I want to confine my discussion to "x + y" in the source thread of this riddle.]

mike the wiz, on 06 Nov 2015 - 12:41 PM, said:

...
You have 5 bottles on a table from left to right. One of them has poison in, you have to find out which one. I will number each object from left to right, from 1 to 5 like in this picture;

bottles.jpg

You deduce which number bottle it is from the following information;

- The poison is in a round bottle that is small.
- The bottles at each end of the table are large bottles, and there are no other large bottles on the table.
- There is a large bottle next to the poisoned bottle.
- One bottle is a cylindrical shape
- Bottle number 2 is not cylindrically shaped
- The poisoned bottle is not next to a cylindrically shaped bottle

Which bottle number is the poison?

(this is not really aimed at you Schera, but at anyone who wants to have a go at solving the riddle using deductive reasoning.)

.
mike the wiz, on 06 Nov 2015 - 5:10 PM, said:

Okay, I can't resist giving the answer, it is in the text below this sentence, you have to highlight the text, I made it invisible in case people still want to figure it out without knowing the answer:

It can't be bottles 1 or 5 as they are large bottles, and the bottle of poison is a small round bottle. It can't be bottle 3 because the bottle of poison is next to a large bottle. So the bottle of poison can only be either bottle 2 or 4. Since bottle 2 can't be a cylindrical bottle and the bottle of poison is not next to a cylindrical bottle then the bottle of poison must be bottle 2 because if it was bottle 4 then the cylindrical bottle would have to be next to it since bottle 2 is not cylindrical, and it was stated that the bottle of poison does not have a cylindrical bottle next to it.

.
(I have yet to view the answer.) If you had specified that the poison is in liquid form, then I would have choosen the one that isn't empty as you haven't specified that the others contain anything.

My highlight above. I think it is assumed that all the bottles have liquid and the poison is in liquid form; it would be a rather simple exercise otherwise.

<snip>

- The poison is in a round bottle that is small.

If its possible for a bottle to be round and small, can't a bottle also be large and cylindrical? What if bottle #1 was large and cylindrical?

Not to be difficult, but I think that is what other posters are saying.

### #7 mike the wiz

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Posted 09 November 2015 - 06:40 AM

Sneakyguy: If its possible for a bottle to be round and small, can't a bottle also be large and cylindrical? What if bottle #1 was large and cylindrical?

Not to be difficult, but I think that is what other posters are saying.

Perhaps you and Goku and the others have found a small technicality.

I should have said that both the "large" bottles were not cylindrical. Perhaps I should have said "two large identical bottles".

It wasn't meant as a red-herring, cylindrical bottles usually aren't best described as "large". Ordinarily I would think of a large bottle as the usual large bottle shape, like large bottles of coca cola. But what I meant by "cylindrical" was a thin bottle, like a bottle of perfume. Usually small bottles of deodorant are cylindrical, they are usually "tall" but I wouldn't usually think of them as, "large", so in all honesty it didn't occur to me to make the delineation.

If it's not too late, I suppose you can regard one premise as "two large identical bottles at either end".

### #8 mike the wiz

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Posted 09 November 2015 - 06:48 AM

My apologies to Goku. In fact Goku did make a logical comment, I suppose I am guilty of immediately suspecting his motives to be negative towards me so I didn't pay enough attention.

Which just goes to show what I was saying - logic isn't always easy, even for me. I think technically I did make a logical mistake by assuming people would treat the two large bottles like I thought of them, that they were just standard bottles that were not cylindrical.

### #9 thatsneakyguy

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Posted 09 November 2015 - 07:33 AM

Perhaps you and Goku and the others have found a small technicality.

I should have said that both the "large" bottles were not cylindrical. Perhaps I should have said "two large identical bottles".

It wasn't meant as a red-herring, cylindrical bottles usually aren't best described as "large". Ordinarily I would think of a large bottle as the usual large bottle shape, like large bottles of coca cola. But what I meant by "cylindrical" was a thin bottle, like a bottle of perfume. Usually small bottles of deodorant are cylindrical, they are usually "tall" but I wouldn't usually think of them as, "large", so in all honesty it didn't occur to me to make the delineation.

If it's not too late, I suppose you can regard one premise as "two large identical bottles at either end".

I didn't think it was an intentional red herring; I actually understood what you were trying to convey. No worries.

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### #10 mike the wiz

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Posted 09 November 2015 - 10:28 AM

BOTTLES RIDDLE 2

You have 6 bottles, one with poison in it. They are numbered thus;

The bottle of poison has bottles on both sides of it.
The bottle of poison is next to a bottle that has no bottle on one side of it.
The bottle with poison in it has bottles each side of it that when you add their numbers comes to a total that is double the number of the bottle with poison in it. And when you divide that total you get by half that total, the number you get is the same number as the number you divided it by, and that is the number of the bottle of poison.
The answer as invisible below, just highlight the below space;

The answer is bottle number 2, because if the bottle of poison is bottle 2 then 3 add 1 comes to 4, and if you divide 4 by half of 4 which is 2 then you get 2, which is the same number you divided it by. but if you think the bottle of poison is bottle 5 then when you add 6 and 4 you get 10 and if you divide 10 by half of ten which is 5, you get 2, which is NOT the same number you divided it by.

### #11 Goku

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Posted 09 November 2015 - 05:22 PM

This is my answer and thought process for riddle # 2. I have not looked at the solution yet. You have to highlight below each clue to see my reasoning, the last line of the post has my answer if you want to skip to the end. Also spell check is not working for me at the moment, so brace yourself.

1. The bottle of poison has bottles on both sides of it.

This eliminates bottles 1 and 6.

2. The bottle of poison is next to a bottle that has no bottle on one side of it.

The poison must be next to bottle 1 or 6, therefore the poison is in bottle 2 or 5.

3. The bottle with poison in it has bottles each side of it that when you add their numbers comes to a total that is double the number of the bottle with poison in it.

Bottle 2 is next to numbers 1 and 3;   1 + 3 = 4,  and  4/2 = 2.    2 = 2 is true.

Bottle 5 is next to numbers 4 and 6;   4 + 6 = 10,  and  10/2 = 5.   5 = 5 is true.

Both bottles 2 and 5 pass the test and cannot be eliminated.

4. And when you divide that total you get by half that total,

The total, call it T, is specified in your clue #3 as 4 and 10 for bottles 2 and 5 respectively. We have to take T and divide it by T/2, which can be rewritten as  2T/T.  The Ts cancel leaving you 2 for both bottles. Also 4/2 = 2,  and  10/5 = 2.

5. the number you get is the same number as the number you divided it by, and that is the number of the bottle of poison.

The number we got, 2, must be the same as the number we divided [the total] by. IOW when you divide T by 2 you get 2.  We can write this as  T/2 = 2.  Solve for T and you get 4 (or you can look at the previous step and notice that we have equation 4/2 = 2  where  4 = T). As previously determined bottle 2's T is 4. We can also say that since T equals twice the number of the bottle from clue #3, therefore  T/2  is equal to the number of the bottle. Subtitute 4 for T, and  4/2 = 2. The two methods agree that bottle number 2 has the poison in it.

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### #12 mike the wiz

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Posted 10 November 2015 - 03:32 AM

Goku: Well done. My comments below;

Yes, the tricky thing for me was to find a difference between bottle 5 and bottle 2, so I had to use the numbers each side of them somehow in order to find a difference. Obviously when adding 4+6 the total is 10 but 3+1 is only four so now I saw that when you divided that by half it was the same number for bottle 2. I perhaps could have made it a bit trickier to solve but it can get annoying for the person trying to solve it if it becomes too convoluted.

### #13 thatsneakyguy

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Posted 10 November 2015 - 01:03 PM

Okay so I started a thread for riddles here.

Cheers

### #14 GodlessGamer

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Posted 10 November 2015 - 05:23 PM

Riddles and logic puzzles are a good deal of fun. That's why I love Sudoku. My main problem with the first riddle, Mike, was that when you said the poisoned bottle was round, I thought of the standard, round-bottomed potion bottle. But when you said that one of the bottles was cylindrical, I thought, "Well heck, that would be round, too, technically." So then 4 could be a small, poisoned cylinder, while not having it next to a cylindrical bottle. Hence either 4 or 2 could be the poisoned bottle, and the riddle has two solutions.

I shall have to check out that other thread! ()

### #15 mike the wiz

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Posted 03 December 2015 - 02:39 PM

PATIO RIDDLE. (Difficulty of riddle - medium)

Which person has a patio rather than a lawn.

LAW of the riddle - Only two houses have lawns and only one house has a patio.

Bill, John and Bob, each have either a patio or a lawn.

Could Bill say; "The grass is greener on the other side." (Bill's house is the left house)

Could John say; ""The grass is greener on the other side." (John's house is the middle house)

Could Bob say; "The grass is greener on the other side."( Bob's house is the right house)

The statements would refer to comparing their neighbours lawn on their left, to their neighbours lawn on their right. (They would be stating which neighbours was the greenest, in their opinion) Obviously Bill, John and Bob, are the three middle houses, next to eachother

The three houses are also in the middle of the street so there is a house left of Bill's house and a house right of Bob's house.

### #16 thatsneakyguy

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Posted 08 December 2015 - 07:35 AM

PATIO RIDDLE. (Difficulty of riddle - medium)

Which person has a patio rather than a lawn.

LAW of the riddle - Only two houses have lawns and only one house has a patio.

Bill, John and Bob, each have either a patio or a lawn.

Could Bill say; "The grass is greener on the other side." (Bill's house is the left house)

Could John say; ""The grass is greener on the other side." (John's house is the middle house)

Could Bob say; "The grass is greener on the other side."( Bob's house is the right house)

The statements would refer to comparing their neighbours lawn on their left, to their neighbours lawn on their right. (They would be stating which neighbours was the greenest, in their opinion) Obviously Bill, John and Bob, are the three middle houses, next to eachother

The three houses are also in the middle of the street so there is a house left of Bill's house and a house right of Bob's house.

I don’t get it.

The statements would refer to comparing their neighbours lawn on their left, to their neighbours lawn on their right. (They would be stating which neighbours was the greenest, in their opinion)

From this each neighbor would require a neighbor on the left and right to make a comparison.

If John’s house (in the middle) had a patio then only he “could” make a true statement.

If either Bill or Bob had a patio, then they both “could” make that true statement.

But that would mean John couldn’t.

Basically whoever had the patio “could” make the statement.

If you meant to add that only one person can make a true statement, then I guess John has the patio.

### #17 mike the wiz

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Posted 08 December 2015 - 09:19 AM

Sneakyguy: From this each neighbor would require a neighbor on the left and right to make a comparison.

"Obviously Bill, John and Bob, are the three middle houses, next to each other"... "there is a house left of Bill's house and a house right of Bob's house"  This just means that Bill, John and Bob's houses are next to each other but that those three houses also have a house either side of them. That's all I meant.

Basically whoever had the patio “could” make the statement.

....

if you meant to add that only one person can make a true statement, then I guess John has the patio.

No, I didn't mean to.

-  Part of a riddle can be finding out what the riddler means. In this case I mean "who can state it?" which is actually a clue to solving it.

Is your answer your "guess" of "John", or would you like to puzzle it out some more? Study it closer and you will get it.

(Think hard about each premise - this is a fairly difficult riddle, if they are made too easy then basically there is no point in the riddle. This one is solved by satisfying all of the premises.)

### #18 thatsneakyguy

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Posted 08 December 2015 - 12:12 PM

Ok, I definitely have my head scratching with that one.

So I ruled out comparing the “greenest” of the lawns.  It doesn’t matter because that is opinion.

And I assumed that even though Bill and Bob are on the right and left, they both had an unknown neighbor with a lawn next to them.

And I assume you mean “how could all three say the above and also it be a true statement”.
Because obviously they could say anything they wanted to, whether it was true or not.  As long as they can speak, all three could say it.

The only other solution I could think of was if they were all standing in one yard, but that wouldn’t make sense because the statements are comparing their neighbor’s yard.

As far as who could state it (and not be lying), I think I answered that. Either both Bill and Bob, or just John.

I am going to hold off on googling it for now…

### #19 mike the wiz

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Posted 08 December 2015 - 12:33 PM

Thatsneakyguy, there is nothing to google, I invented this riddle, as I invented the bottles riddle and the second bottles riddle.

Perhaps I am not the most eloquent of people. To my mind it was enough that I asked, "could", for obviously (at least to my mind) the whole point of the question was to indicate that the one who could say it, gives an answer to the riddle. Here is the answer below, highlight it to see it if you want to see it:

Because Bill, John and Bob's houses are next to each other, with John in the centre house, and another house is each end with no named owners, and since Bill, John and Bob definitely have either a lawn or a patio, and there are only two lawns and one patio present, then logically this means that the two un-named end-houses, can't possible have a patio or a lawn because there are only two lawns and one patio, and after all a house doesn't have to have a patio or lawn;

So if Bill has a patio, then John and Bob MUST have lawns because each either has a patio or lawn and there is only one patio and two lawns. Same if John is the one with the patio, that would mean Bill and Bob would have to have lawns..

So then you can deduce that the two outer houses have neither lawn nor patio.

With that in mind, now you are asked, "who can state the grass is greener?" implying a clue to solve the riddle. Bill can't state it, nor Bob, because Bill and Bob both have a neighbour on one side of them without a lawn or patio. But because I imply someone can state it, then only John can state it but only if he has a patio, because if John had a lawn he would be comparing a patio on one side of him, to a lawn on the other side of him, but if he had a patio, then he could compare Bills' lawn to Bob's lawn, which satisfies all of the premises of the riddle.

### #20 mike the wiz

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Posted 08 December 2015 - 12:48 PM

WHODUNNIT. (just a quick silly one)

Three people and a corpse in a house, one of them is the murderer. Deduce which person is the murderer.

-The person was murdered at exactly 9pm in the kitchen.

- At exactly 9pm Jane was in the bath tub.(bathroom)

- At exactly 9pm Bob was in the living room (lounge)

- At exactly 9pm Paul was in the kitchen.

- Paul was not the murderer

Whodunnit?

Answer below, highlight to see it:

The person I haven't named was the murderer. Paul was the victim.  Lame riddle. Lol

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