# A Riddle Using Deductive Reasoning

132 replies to this topic

### #21 mike the wiz

mike the wiz

Veteran member

• Veteran Member
• 3,384 posts
• Gender:Male
• Interests:mikey mischief.
• Age: 36
• Christian
• Creationist
• England

Posted 06 January 2016 - 11:27 AM

I've just watched an old Die-Hard movie and it had this riddle. It's one of those annoying ones that is "easy" if you see it. But I am not the quickest person on earth and the sucker had me foxed for 20 minutes until I saw the answer and thought; "oh my goodness, the answer was sitting in front of me ringing a bell and waving a flag".

Here it is: (time to annoy yourself)

You have a 5 gallon bottle and a 3 gallon bottle, and you have to get exactly 4 gallons of water. There is a pond full of water for you to use, but you have to get exactly 4 gallons using the bottles.

### #22 piasan

piasan

Veteran Member

• Veteran Member
• 2,742 posts
• Gender:Male
• Location:Oklahoma
• Age: 71
• Christian
• Theistic Evolutionist
• Oklahoma

Posted 06 January 2016 - 12:05 PM

Almost too easy.....

fill the 5 gallon bottle

use it to fill the 3 gallon bottle.

That leaves 2 gallons in the 5 gallon bottle.

Dump the 3 gallon bottle and put the 2 gallons from the 5 in it.

Fill the 5 gallon bottle.

Use one gallon from the 5 to fill the 3.

That leaves 4 gallons in the 5 gallon bottle.

### #23 thatsneakyguy

thatsneakyguy

Junior Member

• 83 posts
• Age: 35
• no affiliation
• Atheist
• Maryland

Posted 08 January 2016 - 09:32 AM

Funny, I had a different solution.

Fill the 3 gallon bottle with water and pour it into the 5 gallon - but do it 2 times.
The second time you fill up the 5 gallon bottle the 3 gallon bottle will have 1 gallon left in it.
Then completely empty the 5 gallon bottle.
Pour the one gallon of water left in the 3 gallon bottle into the 5 gallon bottle.
Then fill the 3 gallon bottle, and add it to the 1 gallon of water that's left in the 5 gallon bottle.

• mike the wiz likes this

### #24 piasan

piasan

Veteran Member

• Veteran Member
• 2,742 posts
• Gender:Male
• Location:Oklahoma
• Age: 71
• Christian
• Theistic Evolutionist
• Oklahoma

Posted 08 January 2016 - 10:59 AM

Funny, I had a different solution.

Fill the 3 gallon bottle with water and pour it into the 5 gallon - but do it 2 times.
The second time you fill up the 5 gallon bottle the 3 gallon bottle will have 1 gallon left in it.
Then completely empty the 5 gallon bottle.
Pour the one gallon of water left in the 3 gallon bottle into the 5 gallon bottle.
Then fill the 3 gallon bottle, and add it to the 1 gallon of water that's left in the 5 gallon bottle.

Yep, that works too..... I guess it's the old "there's more than one way to skin a cat" thing.....

### #25 mike the wiz

mike the wiz

Veteran member

• Veteran Member
• 3,384 posts
• Gender:Male
• Interests:mikey mischief.
• Age: 36
• Christian
• Creationist
• England

Posted 23 January 2016 - 03:08 AM

Again, I'm not going to make it too easy so for this riddle you can't ask me if your answer is right, you just have to figure out your answer using a bit of common sense, too. (This is a riddle I invented)

THE BICYCLE RIDDLE (minimalist information riddle. Difficulty: hard, I hope.)

You have a standard type of bicycle with standard gears, and it has a 50 tooth chain-ring. (the part you pedal) The circumference of the rear wheel is one meter. You rotate the chain-ring one whole revolution. (360 degrees).

How far did you travel? One meter, two meters or three meters?

### #26 Fjuri

Fjuri

Veteran Member

• Veteran Member
• 1,888 posts
• Gender:Male
• Age: 31
• no affiliation
• Atheist
• Belgium

Posted 27 January 2016 - 07:25 AM

Can't solve it. Can you answer these questions:

Is the answer supposed to be included in the "One meter, two meters or three meters"?

What is a standard type of bicycle in your place? a multiple gear bike, or a single gear bike?

A standard bike where I come from, keeps going until you brake (or something else stops the bike), is it the same with you?

You need the gear ratio, this should never be an integer, so a single front rotation should never result in an integer amount of rotations of the rear wheel. (not really a question, an objection)

### #27 mike the wiz

mike the wiz

Veteran member

• Veteran Member
• 3,384 posts
• Gender:Male
• Interests:mikey mischief.
• Age: 36
• Christian
• Creationist
• England

Posted 27 January 2016 - 08:06 AM

Fjuri, thanks for having a go. What I mean by standard gears is just the ordinary looking bicycle, that will usually have say seven or ten gears on the back. All I meant was this bicycle would be your usual bicycle (to look at, it would not look any different from the average bike with gears).

As for integers, don't over-complicate it. Remember, the puzzle isn't going to obey the laws of nature or conform to the rules and regulations of the cycling association for gearing on bicycles. Remember, it is in essence, just a simple puzzle. Simple but a bit difficult.

What you have mentioned tells me you are going in the right direction for solving it, if you add a bit of common sense and think about the clue that this bike would look ordinary, then you might be able to rule out one of those options.

​It will take some thinking, I tried to make it hard to solve which means I have to be a bit ambiguous, and perhaps a touch unfair.

### #28 piasan

piasan

Veteran Member

• Veteran Member
• 2,742 posts
• Gender:Male
• Location:Oklahoma
• Age: 71
• Christian
• Theistic Evolutionist
• Oklahoma

Posted 27 January 2016 - 08:56 AM

I was going to point out the same thing as Fjuri....  There isn't enough information to solve the problem.

I did figure we're talking about the old style "coaster bike" that is only one speed, rather than an 8 or 10 speed bike.  This simplifies the problem because there would be only one sprocket on the drive wheel.

In order to solve it, you need the number of teeth on the rear (drive) wheel, not just the teeth on the sprocket.  Once you have that, the distance calculation is simple.  If the sprocket on the drive wheel has 50 teeth, the distance would be 1 meter; with 25 teeth, it would be 2 meters; with 17 teeth it would be just under 3 meters.

I saw no way to determine the number of teeth on the drive wheel.

### #29 mike the wiz

mike the wiz

Veteran member

• Veteran Member
• 3,384 posts
• Gender:Male
• Interests:mikey mischief.
• Age: 36
• Christian
• Creationist
• England

Posted 27 January 2016 - 09:25 AM

Piasan, you basically almost have the answer, you are a whisker away from the answer and it is highlighted below if you want to read it, or if you want to puzzle it out some more you can read it when you're ready, here it is, highlight to see:

The answer is 2 meters, because if you travelled one revolution and travelled a meter, you would have a rear gear that has 50 teeth, like the chain ring on the front, and on standard bikes that would be unusual to say the least,(I THINK they don't make them that big)as usually the gears are smaller than the chain-ring on the front on standard bikes. it can't be three meters because 50 divided by 3 would give you a gear with 16.6 teeth and the gear sprocket obviously can't have 16.6 teeth, therefore it has to be two meters because then you could have a gear with 25 teeth. Well, perhaps a bit of a silly riddle but there you have it.

### #30 piasan

piasan

Veteran Member

• Veteran Member
• 2,742 posts
• Gender:Male
• Location:Oklahoma
• Age: 71
• Christian
• Theistic Evolutionist
• Oklahoma

Posted 27 January 2016 - 10:30 AM

Piasan, you basically almost have the answer, you are a whisker away from the answer and it is highlighted below if you want to read it, or if you want to puzzle it out some more you can read it when you're ready, .....

I was kind of figuring on the answer you gave.  Fifty teeth on the drive wheel offers no advantage to the bicycle.  Ten teeth would give you a distance of 5 meters, but it would be really hard to start out and almost impossible to ride uphill.

### #31 mike the wiz

mike the wiz

Veteran member

• Veteran Member
• 3,384 posts
• Gender:Male
• Interests:mikey mischief.
• Age: 36
• Christian
• Creationist
• England

Posted 27 January 2016 - 11:16 AM

Yeah, the ratio I am peddling on my new bike is 2.43, which is a 39 chainring and 16T sprocket, but I have a number of gears to choose from but going up hill is always tough on a bike, my old bike I had to just stand up out of the saddle...yeah 50T on the back might be needed if you were going to pedal, oh...I don't know,... up the side of a building perhaps.

### #32 keysi

keysi

Member

• Veteran Member
• 258 posts
• Gender:Male
• Interests:Zooloogy, Anthropology, Psychology, Books, Video Games, Martial Arts.
• Age: 27
• no affiliation
• Agnostic
• United Kingdom

Posted 27 January 2016 - 01:12 PM

I never realised I know so little about gears on a bike haha.

### #33 mike the wiz

mike the wiz

Veteran member

• Veteran Member
• 3,384 posts
• Gender:Male
• Interests:mikey mischief.
• Age: 36
• Christian
• Creationist
• England

Posted 27 January 2016 - 03:48 PM

Keysi: I never realised I know so little about gears on a bike haha.

So if we had a 50 tooth chainring, and 25 teeth on the rear gear sprocket, then with one complete turn of the chain ring you would turn the rear wheel twice because 2 X 25 are 50. It would be a lot harder to move the wheel on say 12 teeth because there is much less torque available and human legs can only push so much torque, so big strong guys can push those big gears. (not me)

Those guys on the time-trial bikes in the Tour-de-France, they pedal with a huge chain ring, maybe 55 teeth, and say a 13 tooth on the back, which means if you were starting off from the traffic lights it would take a big effort just to get the legs going round, but once you get up to speed you can do over 30mph. It's the dichotomy of "torque or speed". If you go for torque, you can pedal small gears but you end up spinning your legs very fast and the bike can only go so fast. So it's torque for hills, speed for flat.

• Goku likes this

### #34 Fjuri

Fjuri

Veteran Member

• Veteran Member
• 1,888 posts
• Gender:Male
• Age: 31
• no affiliation
• Atheist
• Belgium

Posted 28 January 2016 - 03:10 AM

This objection needs to be corrected:

"You need the gear ratio, this should never be an integer, so a single front rotation should never result in an integer amount of rotations of the rear wheel. (not really a question, an objection)"

The reason of my objection was wear.  But as long as the number of links in the chain is no multiple of 2 or 5, it should be ok.

When 2 gears (including chains) interact, having no common divisions is a requirement. Say you have a 50 tooth gear and a 100 link chain, each tooth will interact with exactly 2 links only, which means that any damage to either a tooth or a link will be interacted with only a single tooth or link which will damage that one. The effect will be other way around as well causing massive focused damage, which will cause the gears/chains to break.

Similarly, when you have a 50 tooth gear and a 25 tooth gear after a chain, damage to a single tooth will cause a small shift in torque on each rotation. This small shift in torque will always be applied at the same teeth in the second gear. The effect is smaller when compared to a direct relationship. This is applied in machine construction, but I have learned it isn't applied for applications such as a bike, the effect is negligible or the cost to replace gears is relatively small.

### #35 mike the wiz

mike the wiz

Veteran member

• Veteran Member
• 3,384 posts
• Gender:Male
• Interests:mikey mischief.
• Age: 36
• Christian
• Creationist
• England

Posted 28 January 2016 - 05:51 AM

Fjuri, so you are basically saying that the integerity of my riddle is still intact?

Here is riddle, which likely has MANY correct answers.

You come up to two passageways with a door in front of each, and a guard on each door, you have to go down one of the passages. One leads to freedom the other leads to death. One guard always lies, one guard always tells the truth. The first guard says, "my way leads to freedom". The other guard says, "my way leads to freedom".

You can ask one guard one question in order to determine which path to take. What question will you ask?

(this riddle is just to test our ability to think with ingenuity, there is no correct answer, just as long as you come up with an answer that works...it's probably one of my silly riddles no doubt as I didn't put much thought into it. So if it's a rubbish riddle then you have my disclaimer.

### #36 Fjuri

Fjuri

Veteran Member

• Veteran Member
• 1,888 posts
• Gender:Male
• Age: 31
• no affiliation
• Atheist
• Belgium

Posted 28 January 2016 - 06:57 AM

Yes, I stated my technical objection was not warranted. When I'm wrong I'm wrong.

Are you claiming authorship for that riddle?? How old are you? I know the answer to that famous riddle so I won't post it.

Here's one I like:

Once there was a prince who was the nicest person in the kingdom. His father though is a very nasty person, and whenever the prince tried to give money to the poorest people the king would snap and punish both the boy and the poor. One day, the king got tired of the prince's nice doings and locked him down in the castle dungeon. The wealthy of the neighbors got suspicious of the prince's disappearance, and the king got scared they would hire a lawyer. So, the next day he called all the people in the kingdom for a meeting. He told the people that he put two grapes in a bag, one purple, one green. He would have the prince pick out a grape, and if it was green he could live; but if it was purple he would be killed. Then, he went into the dungeon to let the prince out. He also, when he thought that no one was looking, sneaked two purple grapes into the bag. What he did not know, was that the prince knew about the two purple grapes. He was let out, and lead to the people. After the whole ritual, the prince survived. Being the nice soul he was, he did not want to embarrass his father and tell the people what he did. So how did he survive?

### #37 mike the wiz

mike the wiz

Veteran member

• Veteran Member
• 3,384 posts
• Gender:Male
• Interests:mikey mischief.
• Age: 36
• Christian
• Creationist
• England

Posted 28 January 2016 - 11:02 AM

Fjuri: Once there was a prince who was the nicest person in the kingdom. His father though is a very nasty person, and whenever the prince tried to give money to the poorest people the king would snap and punish both the boy and the poor. One day, the king got tired of the prince's nice doings and locked him down in the castle dungeon. The wealthy of the neighbors got suspicious of the prince's disappearance, and the king got scared they would hire a lawyer. So, the next day he called all the people in the kingdom for a meeting. He told the people that he put two grapes in a bag, one purple, one green. He would have the prince pick out a grape, and if it was green he could live; but if it was purple he would be killed. Then, he went into the dungeon to let the prince out. He also, when he thought that no one was looking, sneaked two purple grapes into the bag. What he did not know, was that the prince knew about the two purple grapes. He was let out, and lead to the people. After the whole ritual, the prince survived. Being the nice soul he was, he did not want to embarrass his father and tell the people what he did. So how did he survive?

Was it by eating the grapes?

If the king sneaked in two purple grapes and there was already one purple and one green then there would be a total of three purple grapes and a green grape. If the prince "knew" about the two additional purple grapes, he could eat the three purple ones.

If I am wrong then my second answer is that there was a second prince perhaps? Someone that told him and swapped the grapes to two green or gave him the green grape.

Oh well I tried, ..

### #38 piasan

piasan

Veteran Member

• Veteran Member
• 2,742 posts
• Gender:Male
• Location:Oklahoma
• Age: 71
• Christian
• Theistic Evolutionist
• Oklahoma

Posted 28 January 2016 - 11:09 AM

Here's one I like:

Once there was a prince who was the nicest person in the kingdom. His father though is a very nasty person, and whenever the prince tried to give money to the poorest people the king would snap and punish both the boy and the poor. One day, the king got tired of the prince's nice doings and locked him down in the castle dungeon. The wealthy of the neighbors got suspicious of the prince's disappearance, and the king got scared they would hire a lawyer. So, the next day he called all the people in the kingdom for a meeting. He told the people that he put two grapes in a bag, one purple, one green. He would have the prince pick out a grape, and if it was green he could live; but if it was purple he would be killed. Then, he went into the dungeon to let the prince out. He also, when he thought that no one was looking, sneaked two purple grapes into the bag. What he did not know, was that the prince knew about the two purple grapes. He was let out, and lead to the people. After the whole ritual, the prince survived. Being the nice soul he was, he did not want to embarrass his father and tell the people what he did. So how did he survive?

Would this be like the carnival shell game.... there is one pea hidden under one of three shells.  Of course the one doing the trick slips the pea out, so there is no pea under any shell.  The win is to pick two shells, say "It's not under either of these." and lift the two shells.   Without revealing the third shell has no pea.  The carnival worker is pretty much forced to grant the "win."

In similar fashion, the prince reaches into the bag and says: "It's not the one I'm pulling out."  When he pulls out a purple grape, it follows the one left in the bag must be green.

### #39 Fjuri

Fjuri

Veteran Member

• Veteran Member
• 1,888 posts
• Gender:Male
• Age: 31
• no affiliation
• Atheist
• Belgium

Posted 29 January 2016 - 02:30 AM

There are exactly 2 grapes in the back. Both are purple. After the king has inspected the bag, nobody else was allowed to touch it.

If he ate all the grapes, no judgement could be made and he'd be guilty by default.

It is an arbitrary Divine Judgement. That means the meaning of the grapes can't be switched, a purple grape is guilty, a green grape is not-guilty. A prince can't change God's methods.

You're really, really close though.

Hint: It are grapes, not balls, or even apples.

Solution:

He takes a grape and quickly swallows it before anyone can see. In order to see which grape he ate, they check the bag and see a purple grape is left. He must have picked the green one..

• mike the wiz likes this

### #40 mike the wiz

mike the wiz

Veteran member

• Veteran Member
• 3,384 posts
• Gender:Male
• Interests:mikey mischief.
• Age: 36
• Christian
• Creationist
• England

Posted 29 January 2016 - 03:53 AM

That is a good one Fjuri, haha. Quite a tricky one, I wouldn't have got it. I like that one.

However, logically speaking, - how would the prince know about the grapes if nobody was allowed to touch the bag? If the king inspected the bag last and nobody saw afterward then the only way the prince could know about the two purple grapes is if the king told him. Nobody else knew, and the prince was not allowed to touch the bag.

But if the king told the prince he would give the game away so it would make no sense for the king to tell the prince or the prince would request the bag was checked first, before the people.

Good riddle but it seems to me there is a logical hole in it. "I win...I always win.....is there no-one on this planet to even challenge me?" - General Zod,- Superman 2.

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users