Solution:

12 steps:

Steps 11 Liter jug 6 Liter Jug
1. 11 -
2. 5 6
3. 5 0
4. 0 5
5. 11 5
6. 10 6
7. 10 0
8. 4 6
9. 4 0
10. 0 4
11. 11 4
12. 9 6 ==> i found 9 liter in 11liter jug(as required)

Solution:

Steps:
1) Light fire on first bar from both the ends and second bar from one end.

2) After 30 seconds(when first bar gets completely burned out) , burn the second bar from second end as well.

3) When second run completely gets burned , you know its 45 seconds.

Solution:

For this answer is 3^0, 3^1, 3^2... That is 1,3,9,27,81,243 and 729.

Solution:

1. Fill 5 liters jar ( 5l-jar:5, 3l-jar:0)
2. Transfer to 3 liters pail (5l-jar:2, 3l-jar:3)
3. Empty 3 liters jar ( 5l-jar:2, 3l-jar:0)
4. Transfer 2q from 5 pail to 3 pail (5l-jar:0, 3l-jar:2)
5. Fill 5 liters pail(5l-jar:5, 3l-jar:2)
6. Transfer 1q from 5 pail to 3 pail(5l-jar:4, 3l-jar:3)

Solution:

Light both the ends of the first string and one end of the second string. 30 minutes will have passed when the first string is fully burned, which means 30 minutes have burned off the second string. Light the end of the second string and when it is fully burned, 45 minutes will have passed.

Solution:

1. Start both the 7 minute hour glass & 11 minute hour glass.
2. Wait till the 7 minute hour glass times out. Time is 7 minute!
3. Restart the 7 minute hour glass. At this time 11 minute hour glass will have 4 minutes left to time out.
4. As soon as 11 minute glass times out invert the 7 minute hour glass. Total time now is 11 minutes.
5. After inverting 7 minute hour glass, it will now have 4 minutes left for time out.
6. After these 4 minutes times out, the total time is 15 minutes.

Solution:

Steps:
* Start both sand measuring glasses at the same time.
* You flip over the small sand hourglass when it finishes the first 5 hours.
* Flip over the large one when it finishes its first 7 hours.
* When the small sand hourglass runs to 10 hours, flip over the small and large sand hourglass at the same time. It means the large sand hourglass will run 3 hours again. When the large sand hourglass run to 13 hours (7 + 3 + 3), flip both the small and large sand hourglass over again to run another 3 hours.

Solution:

Step1 -> Start running both the hourglasses.
Step2 -> When 4 hours hourglass runs out, turn it over.
Step3 -> When 7 hours hourglass runs out, turn it over.
Step4 -> Again when 4 hours hourglass runs out, turn 7 minute hourglass over (it was running for exactly one minute.)
final step -> 8 minute already passed and allow one minute of 7 hour glass to get over. ==>9 minute

Solution:

This is simply the numbers 2^0,2^1,2^2 ... that is 1,2,4,8,16... So for making 1000 kg we need up to 1, 2, 4, 8, 16, 32, 64, 128, and 512

Solution:

Step 1) Pour 1 liter of Water from gallon A to gallon C. Now 4 liter of Water is left in the gallon A and gallon C is full.

Step 2) Pour Water from gallon C to gallon B. Now as soon as gallon B is full , you know there is one liter of Water is in gallon C.