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Topic: You have a jug that holds five gallons (Read 5796 times) |
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UgoLocal02
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You have a jug that holds five gallons
« on: Jun 12th, 2014, 2:17am » |
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You have a jug that holds five gallons, and a jug that holds three gallons. You have no other containers, and there are no markings on the jugs. You need to obtain exactly seven gallons of water from a faucet. How can you do it?
Second Problem: You need exactly four gallons. How do you do it?
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Lupin
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Re: You have a jug that holds five gallons
« Reply #1 on: Jul 5th, 2014, 6:57pm » |
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Wonder why no one has tackled this one.
For seven (and four) gallons: Fill 5-gallon jug. From this jug, fill 3-gallon jug. Two gallons are left on 5-gallon jug. Empty 3-gallon jug. Transfer contents of 5-gallon jug into 3-gallon jug. Now fill 5-gallon jug with water. You have exactly seven gallons (5+3) If you need four gallons, then fill 3-gallon jug (which contains 2 gallons) from 5-gallon jug and four gallons are left on 5-gallon jug.
Can you measure exactly 1, 2, 3, 4, 5, 6, 7, 8 gallons? 
OK, so not exactly let’s say approximately
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rloginunix
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Re: You have a jug that holds five gallons
« Reply #2 on: Jul 5th, 2014, 7:55pm » |
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total capacity.liters now. remaining capacity, e.g 3.2.1 = 3-liter jug has 2 liters in it and can fit 1 more liter.
Exactly:
8: 3.3.0 + 5.5.0
7: 5.5.0 - 3 -> 3.0.3 = 5.2.3, 3.3.0; 3.0.3; 5.2.3 - 2 -> 3.0.3 = 3.2.1, 5.0.5; 5.5.0
6: 3.3.0 - 3 -> 5.0.5 = 3.0.3, 5.3.2; 3.3.0 - 2 -> 5.3.2 = 3.1.2, 5.5.0
5: 5.5.0
4: 5.5.0 - 3 -> 3.0.3 = 5.2.3, 3.3.0; 3.0.3; 5.2.3 - 2 -> 3.0.3 = 3.2.1, 5.0.5; 5.5.0 - 1 -> 3.2.1 = 3.3.0, 5.4.1
3: 3.3.0
2: 5.5.0 - 3 -> 3.0.3 = 5.2.3, 3.3.0
1: see 6.
[edit]
Hid number 2 as per dudiobugtron's notice.
By doing the number six in a more laborious way I was able to reuse it for number one.
Somehow I've totally missed the discussion that followed after my post.
Sorry.
[/edit]
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| « Last Edit: Aug 19th, 2014, 12:40pm by rloginunix » |
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EdwardSmith
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Re: You have a jug that holds five gallons
« Reply #3 on: Jul 6th, 2014, 2:25am » |
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There are two ways of doing this.
Firstly fill the five gallon jug. Drink one gallon. You are left with 4 gallons.
Or
Fill both jugs. Drink four gallons from the five gallon jug then top it up with the 3 gallon jug.
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Schottland Pension
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dudiobugtron
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Re: You have a jug that holds five gallons
« Reply #4 on: Jul 6th, 2014, 4:11pm » |
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rloginunix - your solution to '2' should be hidden, since it is as likely to help you get 7 as the solution to 4 is. (2 + 5 = 4 + 3)
Also, your solution to 6 has an unnecessary step at the end.  3 + 3 = 1 + 5
A further question: imagine the jugs are constructed such that they can hold any integer number of litres of water less than or equal to their capacity. At the start, they both hold zero litres. The 'extra' negative litres are accessed through a secret compartment, so as well as filling the jugs to capacity, you can also fill them up to zero, and empty them down to zero. Can you get a jug with -1 litres? Can you get a jug to contain any arbitrary n < 0 ?
on Jul 6th, 2014, 2:25am, EdwardSmith wrote:There are two ways of doing this.
Firstly fill the five gallon jug. Drink one gallon. You are left with 4 gallons.
Or
Fill both jugs. Drink four gallons from the five gallon jug then top it up with the 3 gallon jug. |
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I like these answers aesthetically. But of course unless you yourself are a measuring jug, you can't determine how many gallons you have consumed.
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towr
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Re: You have a jug that holds five gallons
« Reply #5 on: Jul 6th, 2014, 10:07pm » |
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on Jul 6th, 2014, 4:11pm, dudiobugtron wrote:| A further question: imagine the jugs are constructed such that they can hold any integer number of litres of water less than or equal to their capacity. At the start, they both hold zero litres. The 'extra' negative litres are accessed through a secret compartment, so as well as filling the jugs to capacity, you can also fill them up to zero, and empty them down to zero. Can you get a jug with -1 litres? |
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Sure, 5 - 3 - 3
Quote:| Can you get a jug to contain any arbitrary n < 0 ? |
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-2 = 3 - 5
So we can get 0, -1 and -2, and therefor we can get any negative number by just repeatedly removing 3 (after moving the measured amount to 5 if necessary)
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Wikipedia, Google, Mathworld, Integer sequence DB
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lillianj
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Re: You have a jug that holds five gallons
« Reply #6 on: Aug 19th, 2014, 11:59am » |
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confuse for me 
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movie4fun
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Re: You have a jug that holds five gallons
« Reply #7 on: Aug 20th, 2014, 1:01am » |
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First problem- Fill 5 and then fill 3 using the water from 5. then empty 3 and put the two gallon from 5 to 3. and now fill 5 again. you have 7 in total.
Second problem- fill three and put all in 5. then fill 3 again and pour as much as you can to 5. so 5 is full and three has 1. now empty 5 and take the 1 from 3 to 5. and now fill 3 again. in total you will have 4.
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| « Last Edit: Aug 20th, 2014, 1:07am by movie4fun » |
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wakiza33
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Re: You have a jug that holds five gallons
« Reply #9 on: Sep 10th, 2014, 9:09am » |
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A classic.
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Grimbal
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Re: You have a jug that holds five gallons
« Reply #10 on: Sep 12th, 2014, 12:58am » |
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I think I have given the solution somewhere else:
| hidden: | - if A is empty, fill A,
- if B is full, empty B,
- else transfer from A to B.
Continue until you have the wanted quantity in A, B or A+B.
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That works for all 2-bucket problems. It doesn't matter which one is A and which one B.
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Annettagiles
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Re: You have a jug that holds five gallons
« Reply #11 on: Nov 4th, 2014, 3:37am » |
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How is it possible?
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csendra
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Re: You have a jug that holds five gallons
« Reply #12 on: Nov 21st, 2014, 10:51pm » |
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yes agree with the EdwardSmith that Firstly fill the five gallon jug. Drink one gallon. You are left with 4 gallons. Or Fill both jugs. Drink four gallons from the five gallon jug then top it up with the 3 gallon jug.
else i don't think so there is another solution of it
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| « Last Edit: Nov 21st, 2014, 10:51pm by csendra » |
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Littleton
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Re: You have a jug that holds five gallons
« Reply #13 on: Nov 22nd, 2014, 3:55am » |
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Just fill one halfway! 
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anglia
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Re: You have a jug that holds five gallons
« Reply #14 on: Aug 24th, 2015, 10:39pm » |
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Drink one and 7 would be left.
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