The market scales puzzle

 At first, I tried standard addition with four weights, but I could only reach 15 grams (1 + 2 + 4 + 8=15), which wasn't enough.

Then I noticed the crucial rule of the two-pan scale: weights can go on either pan. That means every weight has three states: on the opposite pan (+1), left off (0), or on the same pan as the herbs (-1).

Because of these three states, I needed powers of 3: 1, 3, 9, and 27.

Together, they reach a maximum of 1 + 3 + 9 + 27 = 40 

For example, to weigh 5 grams, put the 9 on the herb side, and 3 + 1 on the other side: 9 - 3 - 1 = 5.

What if it was a one-pan scale?

Without subtraction, you can only add weights. Each weight has just two states: on or off.

This means you are using simple binary math (powers of 2). With five weights (1, 2, 4, 8, and 16), you can only add them together, giving you a maximum limit of 31 grams (1 + 2 + 4 + 8 + 16=31).

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