Two Brothers, Three Utensils: Dividing 8 kg of Milk Equally

 

Problem Statement

Two brothers have 8 kg of milk. They also have three measuring utensils with capacities of 8 kg, 5 kg, and 3 kg. Using only these utensils, how can they divide the milk into 4 kg each?

🧮 Step‑by‑Step Solution

  1. Start: 8 kg of milk is in the 8 kg vessel.

    • (8, 0, 0)

  2. Pour 5 kg into the 5 kg vessel.

    • (3, 5, 0)

  3. Pour 3 kg from the 5 kg vessel into the 3 kg vessel.

    • (3, 2, 3)

  4. Pour 3 kg from the 3 kg vessel back into the 8 kg vessel.

    • (6, 2, 0)

  5. Pour 2 kg from the 5 kg vessel into the 3 kg vessel.

    • (6, 0, 2)

  6. Pour 3 kg from the 8 kg vessel into the 5 kg vessel.

    • (3, 3, 2)

  7. Pour 2 kg from the 3 kg vessel into the 5 kg vessel.

    • (3, 5, 0)

  8. Pour 5 kg from the 5 kg vessel into the 8 kg vessel.

    • (8, 0, 0)

  9. Now repeat the process to split into two equal 4 kg portions:

    • Transfer 5 kg → (3, 5, 0)

    • Transfer 3 kg → (3, 2, 3)

    • Transfer 3 kg back → (6, 2, 0)

    • Transfer 2 kg → (6, 0, 2)

    • Transfer 2 kg into 8 kg vessel → (4, 0, 4)

✅ Final Answer

The brothers can successfully divide the milk into 4 kg each using the 8 kg, 5 kg, and 3 kg utensils.

Comments

Post a Comment

Popular posts from this blog

Four Weights to Measure Any Amount from 1 to 40 kg

  Problem Statement You have a total of 40 kg to divide into four measuring weights . The challenge: Choose the sizes of these four weights so that you can measure every integer weight from 1 kg to 40 kg using combinations of them. 🧮 Step‑by‑Step Solution This puzzle is solved using the binary system (powers of 2) . With 4 weights, the most efficient split is: 1 kg, 3 kg, 9 kg, and 27 kg . Their total = 1 + 3 + 9 + 27 = 40 . Using combinations of these, you can measure any number from 1 to 40 . Verification Examples 1 kg → directly with 1. 7 kg → 3 + 3 + 1 (or 9 − 2). 15 kg → 9 + 3 + 3. 28 kg → 27 + 1. 40 kg → 27 + 9 + 3 + 1. This works because each weight is roughly triple the previous one (balanced ternary logic), ensuring full coverage.
Read more

The Stick Cutting Puzzle

  Problem Statement A man has a stick of 10 feet length . He cuts 1 foot daily from the stick. How many days will it take him to cut the stick completely into 1‑foot pieces? 🧮 Step‑by‑Step Solution The stick is 10 feet long . To make it into 1‑foot pieces , he needs to make 9 cuts (because after 9 cuts, the stick naturally becomes 10 separate 1‑foot pieces). Since he cuts 1 foot daily , it will take him 9 days to finish cutting the stick. ✅ Final Answer It will take the man 9 days to cut the 10‑foot stick into 1‑foot pieces.
Read more

The Cost of Half‑Sized Cloth

   Problem Statement A cloth of 1 meter length and 1 meter width costs ₹100 . If you buy a cloth of ½ meter length and ½ meter width , how much should you pay? 🧮 Step‑by‑Step Solution Area of full cloth (1 m × 1 m): 1 × 1 = 1  square meter Cost = ₹100. Area of half cloth (0.5 m × 0.5 m): 0.5 × 0.5 = 0.25  square meter Cost per square meter: ₹ 100 1 = ₹ 100  per square meter Cost of 0.25 square meter: 100 × 0.25 = ₹ 25 ✅ Final Answer You have to pay ₹25 for a cloth of ½ meter length and ½ meter width .
Read more