A Challenging Two Jugs Puzzle of Measuring 8 Liter of Water

Submitted by Atanu Chaudhuri on Wed, 12/06/2024 - 10:03

Two Jugs Puzzle of Measuring 8 Liter of Water

Measure exactly 8 liter of water using a 11 liter jug and a 6 liter jug. You may fill and empty the jugs as many times using a large tank with enough water.

Recommended time to solve 20 minutes.

The puzzle will test your systematic thinking and logical analysis skills comprehensively. You will enjoy solving it. Don't let go the opportunity to give it a try and improve your problem solving skills.

Solution to the two jugs puzzle of measuring 8 liter of water

With no idea on how to start, I find as only alternative, imagining what should be the situation when the last filling action measures exactly 8 liter water in the 11 liter jug (the 6 liter jug cannot to hold 8 liter).

I found it easy to do (as you also should).

Imagine how 8 liters will be formed in 11 liter jug

The ending situation (End State): 11 liter jug has 2 liter of water, fill 6 liter jug, empty it into 11 liter jug. Equivalent arithmetic equation: (6 + 2) = 8.

First simplified target: how to measure 2 liter in 11 liter jug

This also is not hard to imagine.

11 liter jug has 7 liter of water (and an empty volume of 4 liter) → fill 6 liter jug → empty into 11 liter jug filling it fully, 2 liter remains in 6 liter jug.

Transfer 2 liter of water to 11 liter jug. Equivalent arithmetic: (6 + 7) - 11 = 2.

Second simplified target: how to measure 7 liter in 11 liter jug

I am moving towards the point where I should start actual filling and emptying actions. The steps till now are just analytical imagined steps. Analysis is from End to Start—Working backwards and End state analysis problem solving techniques in joint action.

11 liter jug has 1 liter of water, fill 6 liter jug, empty it into 11 liter jug which makes 7 liter in 11 liter jug. Equivalent arithmetic: (6 + 1) = 7.

Third simplified target: how to get 1 liter in 11 liter jug: Now it is easy

Fill 6 litter jug, empty it into 11 liter jug which has 5 liter of empty volume. Fill the 6 liter jug again and empty it into 11 liter jug. 1 liter remains in 6 liter jug.

Empty 11 liter jug, transfer 1 liter from 6 liter jug to 11 liter jug which has now 1 liter of water. Equivalent arithmetic: (6 + 6) - 11 = 1.

This is Working backwards and End state analysis problem solving power techniques at work together.

With full clarity, I will now start taking the filling up and emptying actions from beginning to end (steps in natural forward direction: working backwards analysis made the forward direction steps easy).

Solution steps for the 2 jugs puzzle of measuring 8 liter water

Step 1: Fill 6 liter jug, empty into 11 liter jug which has now 6 liter water (and 5 liter empty volume).

Step 2: Fill 6 liter jug again and empty it into 11 liter jug filling it completely. 1 liter remains in 6 liter jug.

Step 3. Empty 11 liter jug, transfer 1 liter of water from 6 liter jug to 11 liter jug.

Step 4: Fill 6 liter jug, empty it into 11 liter jug which has now 7 liter water (and 4 liter empty volume).

Step 5. Fill 6 liter jug and empty it into 11 liter jug filling its empty volume of 4 liters. 2 liter remain in 6 liter jug.

Step 6. Empty 11 liter jug, transfer 2 liter of water to 11 liter jug from 6 liter jug emptying it.

Last step 7: Fill 6 liter jug, empty it into 11 liter jug which has now exactly 8 liter of water.

Can you solve the puzzle in fewer steps? Or, in any other sequence of steps? Explore.

This is a problem rich with learning potential in the area of logical thinking, systematic approach and applying highly effective problem solving techniques, working backwards and end state analysis.