MathDB

(252) 6

Part of 1990 Tournament Of Towns

Problems(1)

TOT 252 1990 Spring A J6 different basic collections of weights

Source:

3/12/2021
We call a collection of weights (each weighing an integer value) basic if their total weight equals 200200 and each object of integer weight not greater than 200200 can be balanced exactly with a uniquely determined set of weights from the collection. (Uniquely means that we are not concerned with order or which weights of equalc value are chosen to balance against a particular object, if in fact there is a choice.) (a) Find an example of a basic collection other than the collection of 200200 weights each of value 11. (b) How many different basic collections are there?
(D. Fomin, Leningrad)
combinatoricsweighings