3 logic problems for the price of one

problem 1
A version of this I saw on the labrinth except this one is a lot more complicated (I think I might have seen it on a website while I was transversing or something can't remember where tho).

What you got:
3 men 1 who tells the truth 1 who lies and one randomly says yes and no.

The problem:
1 of the men is holding a key and you only get to ask the men three questions.

problem 2
This one's an easy one with many solutions that we did in logic class

What you got:
A 3 liter jug a 5 liter jug, an infinate amount of water, and a big tub (infinately large)

The problem:
you need to fill the big tub with 9 liters of water

problem 3
This one is a math problem I pulled from a website I'll cite it when everything is done:

What you got: the numbers 3 3 7 7

The problem: you need to get 24 using only addition, multiplication, division and subtraction. everything is in base 10 and no decimal's where used and you need to use all 4 numbers only once.

I love those kind of problems. Post more please or email them to me. Thank you.

The first one: Just ask each one "Who has the key?" :D

Second one: Fill the 5 litre jug, pour it into the 3, and the overfill goes into the tub
Repeat once.
Fill and pour the 5 litre jug into the tub :cool:

The last one might take more than 5 seconds...

Must we use all 4 digits?

Because 3*7+3 = 24 :(

Problem 1:
the guy who tells the truth and the guy who lies will always answer predictably so when you find the only one where they say yes/no to, the one random guy will simply say yes/no and if he changes his answer then you know he's the random guy...

Problem 2:
I think you messed up the final size, because getting 9 liters with a 3 liter jug is not hard.. just fill it up 3 times... But if you wanted to do it the hard way, just use the overflow from the 5 to the 3 in order to get 2 liters and then do the math from there.

Problem 3:
hmmm not entirely sure
(3 * 7) + 3 but then there's a 7 left over....

your missing the line where it says you need to use "all 4 numbers once." And you need to get a key I thought that needing to get the key was implyed

Problem 1:

<still working on it>

Problem 2:

Option 1: Fill the three liter jug three times, emptying it each time into the tub.

Option 2: Fill the 5 liter jug and pour it into the 3 liter job, allowing the remaining two liters to overflow into the tub. Do this again, so that you have a total of 4 liters in the tub. Finally, fill the 5 liter container and poor the whole thing into the tub.

Problem 3:

7*(3+3/7) = 24

way to go avdven
I messed up on the second one it's supposed to be 3, 7 and 8 but I'm tired and messed up oh well.

Zepherin: I am unable to find a solution for the first problem. I had it figured out (I figured out who had the key), but in order to actually get the key, it would require a 4th question (or at least a command telling the person with the key to give it to you). I can also figure out who is who (which is the truth teller, which is the liar, and which is the one who answer ambiguously), but, once again, once I have information, getting the key would require another question. Any hints?

AJ

77 - 3 / 6 =24.66666666666666666

but we're not using decimals so 77 - 3 / 6 =24

advens answer looks much more correct (and i thought i tried that!?!)


3 gal jug 3 times

can't get the key yet!

Quote:

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Originally posted here by zepherin
I messed up on the second one it's supposed to be 3, 7 and 8 but I'm tired and messed up oh well. [/B]

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Solution:

Fill 7 liter jug and pour into 3 liter jug, allowing the remaining 4 liters to flow into the tub. Repeat to add another 4 liters, and you have a total of 8 liters.

AJ

ok, now i don't get it.

if you do:

7*(3+3/7) = 24 arn't you using decimels?

3/7 = 0.428571428571428571428

+3 = 3.28571428571428571428

i mean even though the answer is an int your working with (using) decimels. no?

Tedob: You're right... it is using decimals, but I think when he said that you can't use decimals, he meant that the solution must not contain any decimals. Typing the equation into a calculator (for example) using all of the correct parenthesis and such will never display a decimal. The reason I think he said no decimals was so that you don't do what you tried, which was truncating the decimal off of the final answer to get the correct answer. Also, 3/7 is not necessarily a decimal... it's a rational, which is considered a number. It's true that if you divide 3 by 7, you will receive a decimal, but I always learned to leave everything in rational form so as to not lose accuracy by rounding a decimal.

AJ

there's a few solutions to this, here's the one I came up with.

talk to one of the guys ask the guy who is more likely to tell the truth out of the two of those guys.
If the answer is yes/no you have the random guy. If he's the random guy move to the next guy and ask him if the guy which you know is the random guy is the guy who always tells the truth if the answer is yes he's the lyer and move to the truth tell and ask him who has the key if he says no to the question he's the truth teller and then ask him who has the key.

If the answer to the first question comes up as 1 of the two guys, both the consistent lyer and the consistent truth teller will have chosen the random guy because he has a better chance of telling the truth than the constent lyer and is less likely to tell the truth than the constent truth teller. so ask the guy again if they guy he said was the truth teller if the answer is yes than move to the guy that the original guy didn't say and ask him who has the key, if the answer is no than ask the original guy who has the key.

hrmmm, I guess your right you'd need a question if you actually wanted them to give you the key, don't worry I'll get better at this whole proposing questions in a clearer manner thing.

For people who may want an explanation (I could go into a long, logic-based discussion) I found a link which may show how it was done...

http://rinkworks.com/brainfood/s/wd.39.shtml

My answer (which I didn't post because it wasn't what I thought he was looking for) is very similar to this, though I had slightly different questions and a table I created was centered around different propositions.

AJ

sorry for the confusion

Problem #1 and #2 are trivial, hence I'm going to ignore them...

But #3 seems to be stumping people...

Quote:

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Originally posted here by avdven
Problem 3:

7*(3+3/7) = 24

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Since 3/7 is a decimal, I'm assuming this is "illegal" as per "the rules," but...

7*(3+3/7) = 7(21/7 + 3/7) = 7(24/7) = 24

Quote:

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Originally posted here by Tedob1
77 - 3 / 6 =24.66666666666666666

but we're not using decimals so 77 - 3 / 6 =24

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Actually 77 - 3/6 = 76.5

But I think you meant (77-3)/6 which actually is close6 to 12 (74/6 which is 12 1/3 or 12.333333)




I'll have to wake up a little bit and glance at this again - my solution seems to have gone for a walk around the building or something since I first started reading this thread...

3/7 isn't a decimal it's a fraction, and 7(3/7) eliminates it before it becomes a decimal.