## Milkman's dilemma in delivering 1 quart milk each to two jugs of 4 pints and 5 pints

Milkman to put exactly 1 quart milk each to two jugs 4 pints and 5 pints capacity from his two cans full of 10 gallons each milk. Time to solve 20 mins.

### The two jugs riddle of delivering exactly 1 quart milk each

A milkman while going to his dairy met two women. One of them had a jug of 4 pint capacity and the other a jug of 5 pint capacity. They implored the milkman to sell them exactly 1 quart of milk each. The milkman was carrying two cans full of 10 gallons of milk each. But he had no way to measure the 1 quart milk wanted by the women.

Still, being quite a brainy fellow, the milkman managed to put exactly 1 quart milk each to the two jugs of the two women.

In what minimum number of steps could he have done it?

You can transfer any amount of milk between the four containers any number of times.

**Information:** 1 gallon equals 4 quarts and 1 quart equals 2 pints.

**Time to solve:** 20 minutes.

### Solution to the two jugs riddle of delivering 1 quart milk each

If you start thinking of solving it from the beginning with the objective of first putting 2 pints or 1 quart milk in 1 jug and then another quart of milk to the second jug, you will face a kind of barrier that apparently seems impossible to cross.

With 1 quart milk in 1 jug that you cannot use any further, you have the two 10 gallons milk cans and 1 empty jug. How can you put exactly 1 quart milk in this jug?

So this is the real bottleneck or most difficult hurdle to cross.

If it is so, then why not START FROM THE END?

You decide to imagine,

What would exactly be the last few steps to put 1 quart milk to the 4 pint jug, with 1 quart milk already there in the 5 pint jug.

And when you set your mind specifically on ONE PART OF THE PUZZLE, the steps become clear.

**Step last but 2:**

1 quart of milk is already assumed to have been put in the 5 pint jug. You will not use it any further.

You realize at this point that,

If the 4 pint jug is empty and 5 pint jug contains exactly 1 quart milk, this amount of milk must be missing from the two cans. Just fill one can completely and you have exactly 2 pints or 1 quart empty volume in the other can.

This the key pattern. You will fill this 1 quart empty volume in one can from 4 pints jug filled leaving exactly 2 pints as desired.

In the last but second step then you would, Fill first can fully from the second can. With 4 pint jug empty second can has exactly 2 pint volume empty.

**Step last but 1:**

Fill the 4 pint jug fully from 1st can. Now 5 pint jug contains 1 quart milk, 4 pint jug contains 4 pint milk, 1 can has 4 pint empty volume and 2nd can has 2 pint empty volume.

**Last step:**

Fill the 2nd can fully from the filled up 4 pint jug leaving exactly 1 quart of milk in the jug.

This must be the way to the solution. You have no doubt at this point about this.

But have you solved the puzzle?

No, *you have imagined a feasible solution to last part of the riddle*, **assuming that 1 quart of milk is already put in the 5 pint can.**

### Solution to the part of puzzle of putting 1 quart of milk in the 5 pint jug

Now you have broken up the riddle into two parts, imagined a feasible solution to the second and last part, and facing the first part of the riddle.

The problem is reduced in complexity by this problem solving approach.

Not only have you broken down the riddle into two parts, you have also solved the harder part **working backwards** from the END TO THE BEGINNING.

With this new riddle, again you would **resort to imagining the last steps.**

How can you put exactly 1 quart or 2 pints of milk in the 5 pint jug?

Already having a good look at the problem, this part is easy to you now,

With 1 pint of milk in 4 pint jug, you will fill the 4 pint jug from the 5 pint fully filled jug leaving 5 - 3 = 2 pints or 1 quart of milk exactly.

Notice that the riddle is further broken down to a new riddle, how to put 1 pint of milk in 4 pint jug?

But that is very easy for you at this stage. You would just fill the empty 4 pint jug from fully filled 5 pint jug leaving exactly 1 pint in the 5 pint jug. At the next step you would transfer this 1 pint to the 4 pint jug.

### Final solution: Putting all the pieces together

It is high time to put all the pieces together.

**Step 1:** Fill 5 pint jug from 1st can.

**Step 2:** Fill 4 pint jug from fully filled 5 pint jug leaving 1 pint milk in 5 pint jug.

**Step 3:** Empty the 4 pint jug into the 1st can.

**Step 4:** Transfer 1 pint milk from 5 pint jug to the 4 pint jug. Now 5 pint jug is empty and 1 pint empty volume is in 1st can.

**Step 5:** Fill 5 pint jug from 1st can. This can has 6 pint empty volume.

**Step 6:** Fill 4 pint jug from fully filled 5 pint jug leaving exactly 2 pints or 1 quart in it. 1st can still has 6 pint empty volume.

**Step 7:** Empty fully filled 4 pint jug into 1st can. Now 1st can has exactly 2 pints or 1 quart of empty volume.

**Step 8:** Fill 4 pint jug from the second can now.

**Step 9:** Fill the 2 pint empty volume in 1st can from fully filled 4 pint jug leaving exactly 2 pints or 1 quart of milk in it.

You have used **Problem breakdown technique** along with **Working backwards approach** and **End state analysis approach**, all three powerful problem solving techniques.

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