# Minimum Number of Weights Puzzle

## Wholesale Merchant

Ravi owns a vegetable shop where he has to weigh items weighing up to 121 kilograms on a beam balance. He uses a balance scale to weigh the vegetables.

What is the minimum number of weights you think he should carry with him, such that he is able to weigh 121 kilograms, and how heavy should these weights be?

## Minimum Number of weights

Ravi owns a vegetable shop where he has to weigh items weighing up to 121 kilograms on a beam balance. He uses a balance scale to weigh the vegetables.

What is the minimum number of weights you think he should carry with him, such that he is able to weigh 121 kilograms, and how heavy should these weights be?

## Solution

We need to find the minimum number of weights required to weigh 121 kg. And the mode of weighing is a beam balance. By using a beam balance, we get the option to add and subtract weight to form an ideal weight.

To weigh 121, we will use powers of 3.

The combination of powers of 3 which can give us 121 is:

` 3^0, 3^1, 3^2, 3^3 3^4 => 1 + 3 + 9 + 27 + 81 = 121.`

Using these five weights, now we can create any weight between 1-121kgs, by adding and subtracting weight off of the beam balance.

Let us try be weighing any weight, say 120 kg

Then the equation for that will be

` 81 + 27 + 9 + 3 = 120 `

Thus by using  4 of the 5 weights we can weigh 120 kg

Similarly for weight like 73 kg, the equation will be

`81 + 1 = 82 = 73 + 9`

Here on pan we are putting two weights 81 kg and 1 kg, which together weigh 82 kg. Now we want 73 kg, so we will add the 9 kg weight on the balancing pan (opposite side), and we can weigh 73 kg.

Thus by using this method we can basically weigh any weight between 1 to 121 kg, by using only 5 weights.

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• Bulb in the Next Room
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