KCC's Quizzes AQQ292 about weighing using 2-plates scale

Use six weights: 1, 2, 4, 8, 16, 13 gm.

Thanks CiruiTree , but there is a solution with only 4 elements!

Yes, the four-counterweight ternary method is a better solution.  Congratulations to those who found it.

There are solutions with even fewer counterweights:

One-counterweight, model A:  The problem states that we are to weigh amounts of a substance.  Place a 1 gm counterweight on one side of the scale, and enough of the substance on the other side to balance the scale.  Remove the weighed amount and continue weighing 1 gm amounts, and count the weighings.

One-counterweight, model B:  The problem asks us to design a two-dish scale, so we can design the scale with one fixed-length arm, and one adjustable-length arm.  Place a 1 gm counterweight on the adjustable side dish and adjust that arm length to balance the unknown mass on the other dish.  Read the mass from the arm position, similar to a locker room scale.  Design the dish and arm masses to be inconsequentially small in order to neutralize their effect on the reading.

Zero-counterweight:  The puzzle picture shows individual, removable masses as our counterweights.  Design a scale with one adjustable-length arm which uses the masses of its dish and arm as its reference mass.  There are no as-shown counterweights in this solution.

Negative-counterweight:  The puzzle asks for the minimum number of counterweights, which would be an infinitely negative number of them.  We can use helium balloons as negative counterweights by attaching them to the test side of the scale.  An infinite quantity of infinitely-small helium balloons would comprise the minimum number of counterweights.  Given the design challenge of infinity, let's settle for a very large number of teeny-tiny helium balloons.

Interesting!

Interesting!