Almost 3 years back, I had posted a milkman puzzle, which was the second puzzle I posted (https://alokgoyal1971.com/2013/02/10/solution-to-puzzle-2-milkman-puzzle/). Here again is a modified version of the same puzzle. A very interesting puzzle that Alok Mittal gave to his Mathematical Circles class.
A milkman has four jars of the following sizes – 24 litres, 13 litres, 11 litres and 5 litres. The 24 litre jar is full of milk, and the others are empty. He needs to divide the milk into three parts of 8 litres each. Unfortunately, the milkman has no additional markings in the existing jars to be able to figure out how to measure 8 litres. Can you help the milkman?
Please send your answers either directly on the blog site as comments, or to me at alokgoyal_2001@yahoo.com. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.
Happy dividing!
Alok Goyal's Puzzles Page 
Let state be represented by a vector a b c d which represent milk in 24, 13, 11 and 5 ltr jar respectively
The transformation happens as follows:
24 0 0 0
11 13 0 0
11 8 0 5
11 0 8 5
0 11 8 5
0 13 8 3
3 13 8 0
3 8 8 5
8 8 8 0
Great!
The numbers below represent the jars of corresponding sizes (liters). Carry out the following processes. All processes carried out until either the second jar is full or the first jar gets empty before that.
24 to 11
24 to 5
Now 24 liters jar has exactly 8 liters .
5 to 13
11 to 13
13 to 5
Now 13 liters jar has exactly 8 liters.
5 to 11
Now 11 liters jar has exactly 8 liters.
Awesome!
Solution:
24 – 0 – 0 – 0 8 – 0 – 11 – 5 8 – 13 – 3 – 0 8 – 8 – 8 – 0 On 17-Jan-2016 9:20 pm, “Alok Goyals Puzzles Page” wrote:
> Alok Goyal posted: “Almost 3 years back, I had posted a milkman puzzle, > which was the second puzzle I posted ( > https://alokgoyal1971.com/2013/02/10/solution-to-puzzle-2-milkman-puzzle/). > Here again is a modified version of the same puzzle. A very interesting > puzzle that Alok M” >
5 11 13 24
x x x 24 (initial state)
5 11 x 8 (fill up 5 and 11 from 24)
x 3 13 8 (fill up 13 from 5 and remaining from 11)
5 3 8 8 (fill up 5 from 13)
x 8 8 8 (pour 5 into 11)