7, 5 Liter jars 7, 0 = fill 7 liters jar 2, 5 = transfer to the 5 liters jar 2, 0 = emtry the 5 liters jar 0, 2 = transfter to 5 liters jar 7, 2 = fill in the 7 liter jar 4, 5 = transfer 7 liter to 5 liter jar 4, 0 = emtry to 5 liters jar 0, 4 = transfer to 5 liters jar 7, 4 = fill in 7 liter jar 6, 5 = transfer 7 liter to 5 liter jar Fill the 7 liter jar and tip into the 5liter jar. you now have 2 litres in the 7 liter jar, empty the 7 liter and tip the 2 liters into the 5liter jar. Fill the 7liter and tip into 5 liter, you now have 4 liters in the 7 liter jar, empty the 5 liter jar and put 4liters from 7 liter jar into it. Again fill the 7 liter jar, 1 more liter will fill the 5 liter jar so empty the 7 liter into the 5 liter, 6liters left in the 7 liter jar;-)
Solution!!!! 0 13 7 7 13 0 7 6 7 14 6 0 14 0 6 1 13 6 1 12 7 8 12 0 8 5 7 15 5 0 19 1 0 12 1 7 12 8 0 5 8 7 5 13 2 18 0 2 18 2 0 11 2 7 11 9 0 4 9 7 4 13 3 17 0 3 17 3 0 10 3 7 10 10 0 ==== Solution with lesser number of steps: 0 13 7 13 0 7 19 0 1 19 1 0 12 1 7 12 8 0 5 8 7 5 13 2 18 0 2 18 2 0 11 2 7 11 9 0 4 9 7 4 13 3 17 0 3 17 3 0 10 3 7 10 10 0
# Fill the 5 liter bucket # Pour it into the 7 liter bucket # Fill the 5 liter bucket # Fill the 7 liter bucket from the 5 (2 liters go in leaving 3 liters in the 5 liter bucket) # Empty the 7 liter bucket # Pour the 3 liters from the 5 liter bucket into the 7 liter bucket # Fill the 5 liter bucket # Fill the 7 liter bucket from the 5 liter bucket (4 liters go in leaving 1 liter in the 5 liter bucket) # Empty the 7 liter bucket # Pour the 1 liter form the 5 liter bucket into the 7 liter bucket # fill the 5 liter bucket. You now have 5 liters in the 5 liter bucket and 1 liter in the 7 liter bucket; 6 liters in all. Pour the 5 liters into the 7 liter bucket if you want all 6 liters in one container.
You have to have something else to build the 4 liters into. Call it The Tub.Fill the 5.Pour the 5 into the 3.That leaves 2 liters in the 5.Pour them into The Tub. You now have 2 liters in The Tub.Empty the 3.Fill the 5.Pour the 5 into the 3.That leaves 2 liters in the 5.Pour them into The Tub. You now have 4 liters in The Tub.QEDYou do not have a TUB, it is not in the problem.Fill the 5 liter containerPour it into the 3 liter container leaving 2 liters in the 5 liter containerEmpty the 3 liter containerPour the 2 liters from the 5 liter container into the 3 liter containerFill the 5 liter containerFill the remainder of the 3 liter container from the 5 liter containerSince the 3 liter container already had 2 liters in it, one liter from the 5 liter container will fill it leaving 4 liters in the 5 liter container.Solved
Here's a step-by-step solution: Fill up the 5-liter jar completely with water. Pour the water from the 5-liter jar into the 3-liter jar until the 3-liter jar is full. Now, you are left with 2 liters of water in the 5-liter jar. Empty the 3-liter jar. Pour the 2 liters of water from the 5-liter jar into the 3-liter jar. Fill up the 5-liter jar again. Pour enough water from the 5-liter jar into the 3-liter jar to fill it completely (this will take 1 liter). Now, you are left with 4 liters of water in the 5-liter jar, which gives you the required 8 liters of water.
There is most likely a more efficient way to do this, but this is the best I can do for now.Notation: ( x , y ) where x is the amount of water in the 5-liter container and y is the amount of water in the 7-liter container1. Fill the five-liter container ( 5 , 0 )2. Pour the five-liter container into the seven-liter container ( 0 , 5 )3. Fill the five-liter container ( 5 , 5 )4. Fill the seven-liter container with the five-liter container, leaving 3 liters in the five-liter container ( 3 , 7 )5. Pour out the seven-liter container ( 3 , 0 )6. Pour the five-liter container into the seven-liter container ( 0 , 3 )7. Fill the five-liter container ( 5 , 3 )8. Fill the seven-liter container with the five-liter container, leaving 1 liter in the five-liter container ( 1 , 7 )9. Pour out the seven-liter container ( 1 , 0 )10. Pour the five-liter container into the seven-liter container ( 0 , 1 )11. Fill the five-liter container ( 5 , 1 )12. Pour the five-liter container into the seven-liter container ( 0 , 6 )
each row has the contents of 8 5 3 in that order 8 0 0 5 0 3 5 3 0 2 3 3 2 5 1 7 0 1 7 1 0 4 1 3 4 4 0 the other solution is 8 0 0 3 5 0 3 2 3 6 2 0 6 0 2 1 5 2 1 4 3 4 4 0 See related link "Dividing" for more info
7, 5 Liter jars 7, 0 = fill 7 liters jar 2, 5 = transfer to the 5 liters jar 2, 0 = emtry the 5 liters jar 0, 2 = transfter to 5 liters jar 7, 2 = fill in the 7 liter jar 4, 5 = transfer 7 liter to 5 liter jar 4, 0 = emtry to 5 liters jar 0, 4 = transfer to 5 liters jar 7, 4 = fill in 7 liter jar 6, 5 = transfer 7 liter to 5 liter jar Fill the 7 liter jar and tip into the 5liter jar. you now have 2 litres in the 7 liter jar, empty the 7 liter and tip the 2 liters into the 5liter jar. Fill the 7liter and tip into 5 liter, you now have 4 liters in the 7 liter jar, empty the 5 liter jar and put 4liters from 7 liter jar into it. Again fill the 7 liter jar, 1 more liter will fill the 5 liter jar so empty the 7 liter into the 5 liter, 6liters left in the 7 liter jar;-)
7 Liter Bucket | 5 Liter Bucket7 | 03 | 43 | 00 | 37 | 36 | 46 | 02 | 42 | 00 | 27 | 25 | 45 | 0
1. Fill the 3 liter bowl from the 10 liter jug. -Jug: 7/10 -Bowl: 3/3 -Cup: 0/5 2. Pour the 3 liters from the bowl into the 5 liter cup. -Jug: 7/10 -Bowl: 0/3 -Cup: 3/5 3. Fill the 3 liter bowl again from the 10 liter jug. -Jug: 4/10 -Bowl: 3/3 -Cup: 3/5 **If having the 4 liters in the jug is acceptable, just stop here. If you need the 4 liters in the cup, continue. 4. Fill the remainder of the 5 liter cup with with water from the 3 liter bowl. This will use 2 of the 3 liters in the bowl, leaving one left over. -Jug: 4/10 -Bowl: 1/3 -Cup: 5/5 5. Pour the 5 liters in the cup into the jug. -Jug: 9/10 -Bowl: 1/3 -Cup: 0/5 6. Pour the 1 liter from the 3 liter bowl into the 5 liter cup. -Jug: 9/10 -Bowl: 0/3 -Cup: 1/5 7. Fill the 3 liter bowl with water from the 10 liter jug. -Jug: 6/10 -Bowl: 3/3 -Cup: 1/5 8. Pour the 3 liters in the bowl into the 5 liter cup. -Jug: 6/10 -Bowl: 0/3 -Cup: 4/5 You now have 4 liters in the 5 liter cup.
Notes: There is most likely a more efficient way to do this, but this is the best I can do for now.Notation: ( x , y ) where x is the amount of water in the 5-liter container and y is the amount of water in the 7-liter container1. Fill the five-liter container ( 5 , 0 )2. Pour the five-liter container into the seven-liter container ( 0 , 5 )3. Fill the five-liter container ( 5 , 5 )4. Fill the seven-liter container with the five-liter container, leaving 3 liters in the five-liter container ( 3 , 7 )5. Pour out the seven-liter container ( 3 , 0 )6. Pour the five-liter container into the seven-liter container ( 0 , 3 )7. Fill the five-liter container ( 5 , 3 )8. Fill the seven-liter container with the five-liter container, leaving 1 liter in the five-liter container ( 1 , 7 )9. Pour out the seven-liter container ( 1 , 0 )10. Pour the five-liter container into the seven-liter container ( 0 , 1 )11. Fill the five-liter container ( 5 , 1 )12. Pour the five-liter container into the seven-liter container ( 0 , 6 )
1)Transfer 7 liters from the 12-liter jar into the 7-liter jar.We now have 5 liters in the 12-liter jar and 7 liters in the 7-liter jar. The 5-liter jar is empty, as of now.2)Transfer 5 liters from the 7-liter jar into the 5-liter jar.The 12-liter, 7-liter, 5-liter jars now contain 5, 2 and 5 liters respectively.3)Empty the contents of the 5-liter jar into the 12-liter jar.The 12, 7, 5- liter jars now contain 10, 2 and 0 liters respectively.4)From the 7-liter jar, take out 5 liters and pour 7 liters from the 12-liter jar into the 7-liter jar.We now have 3 liters in the 12-liter jar and 7 in the 7-liter one, while the 5-liter jar has only two liters in it.5)Fill up the remainder of the 5-liter jar using the 7-liter jar.That leaves us with 3 liters on the 12-liter jar and 4 liters in the 7-liter jar. The 5-liter jar is full.6)Pour the contents of the 5-liter jar into the 12-liter jar.There are 8 liters in the 12-liter jar and 4 liters in the 7-liter jar, while the 5-liter jar is empty.7)Pour the 4 liters that are in the 7-liter jar into the 5-liter jar.We now have 8 liters in the 12-liter jar and 4 liters in the 5-liter jar. The 7-liter jar is empty.8)Fill the 7-liter jar using the 12-liter jar.There is now only 1 liter in the 12-liter jar and 7 liters in the 7-liter jar and 4 liters in the 5-liter jar.9)Fill up the 5-liter jar using the 7-liter jar.There is now 1 liter in the 12-liter jar and 6 liters in the 7-liter jar and 5 in the 5-liter jar.NOTE: This might not be the only way, or the shortest way to do it.
Solution!!!! 0 13 7 7 13 0 7 6 7 14 6 0 14 0 6 1 13 6 1 12 7 8 12 0 8 5 7 15 5 0 19 1 0 12 1 7 12 8 0 5 8 7 5 13 2 18 0 2 18 2 0 11 2 7 11 9 0 4 9 7 4 13 3 17 0 3 17 3 0 10 3 7 10 10 0 ==== Solution with lesser number of steps: 0 13 7 13 0 7 19 0 1 19 1 0 12 1 7 12 8 0 5 8 7 5 13 2 18 0 2 18 2 0 11 2 7 11 9 0 4 9 7 4 13 3 17 0 3 17 3 0 10 3 7 10 10 0
# Fill the 5 liter bucket # Pour it into the 7 liter bucket # Fill the 5 liter bucket # Fill the 7 liter bucket from the 5 (2 liters go in leaving 3 liters in the 5 liter bucket) # Empty the 7 liter bucket # Pour the 3 liters from the 5 liter bucket into the 7 liter bucket # Fill the 5 liter bucket # Fill the 7 liter bucket from the 5 liter bucket (4 liters go in leaving 1 liter in the 5 liter bucket) # Empty the 7 liter bucket # Pour the 1 liter form the 5 liter bucket into the 7 liter bucket # fill the 5 liter bucket. You now have 5 liters in the 5 liter bucket and 1 liter in the 7 liter bucket; 6 liters in all. Pour the 5 liters into the 7 liter bucket if you want all 6 liters in one container.
The sequence shows the amount of water in each jar for each step: (1) 7-13-0; (2) 19-1-0; (3) 12-1-7; (4) 12-8-0; (5) 5-8-7; (6) 5-13-2; (7) 18-0-2; (8) 18-2-0; (9) 11-2-7; (10) 11-9-0; (11) 4-9-7; (12) 4-13-3; (13) 17-0-3; (14) 17-3-0; (15) 10-3-7; (16) 10-10-0.
Fill the 5 liter container.Pour it into the 8 liter container.Fill the 5 liter container again.Pour it into the 8 liter container again, but stop when the 8 liter container is full.The 5 liter container now contains 2 liters.
Fill the 7 liter bottle. Then put it into the 5 liter bottle. This leaves 2 liters in the big bottle. Empty the 5 liter bottle. put the remaining 2 liters into the 5 liter bottle. Fill the 7 liter bottle again. Again, put it into the 5 liter bottle. This will now leave 4 liters in the big bottle. Empty the 5 liter bottle. put the 4 liters in. Fill the 7 liter bottle one more time. put it into the 5 liter bottle. Since there were already 4 liters in the small bottle, it can only hold 1 more, leaving 6 liters in the big bottle. after that u will win it!!!!!!!! Fill the 5 liter bottle. Then put it into the 7 liter bottle. Fill the 5 liter bottle again and put it into the 7 liter bottle. This will leave 3 liter in the small bottle. Empty the 7 liter bottle and put the 3 liter water from 5 liter bottle to 7 liter bottle. Fill the 5 liter bottle again and put it in 7 liter bottle, only 1 liter will left in the 5 liter bottle. Empty the 7 liter bottle and put the 1 liter from 5 liter bottle to 7 liter bottle. Fill the 5 liter bottle again and empty it into the 7 liter bottle. You will end up with 6 liter in the 7 liter bottle. You Win......