There is one 40 kg weight stone.How many weights are there such that it can measure any weight between 1 to 40

Question

There is one 40 kg weight stone.How many weights are there such that it can measure any weight between 1 to 40 kg?

Answer 1

at least 4 pieces of weights are required. they are 1kg, 3kg, 9kg, and 27kg in weight.

possible interesting weights of such qeer stones and the denominations of the weights are

1kg = 1kg
4kg = 1+3 kg weights
13kg = 1+3+9 kg weights
40kg = 1+3+9+27 kg weights
121kg = 1+3+9+27+81 kg weights and so on...............
This is from Towhid IBA, Dhaka University

Answer 2

at least 4 pieces of weights are required. they are 1kg, 3kg, 9kg, and 27kg in weight.

possible interesting weights of such qeer stones and the denominations of the weights are

1kg = 1kg
4kg = 1+3 kg weights
13kg = 1+3+9 kg weights
40kg = 1+3+9+27 kg weights
121kg = 1+3+9+27+81 kg weights and so on...............
This is from Towhid IBA, Dhaka University