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.

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