Minimum Number of Weights Puzzle

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.