MathDB

(258) 2

Part of 1990 Tournament Of Towns

Problems(1)

TOT 258 1990 Spring A S2 different basic collections of weights, senior version

Source:

6/8/2024
We call a collection of weights (each weighing an integer value) basic if their total weight equals 500500 and each object of integer weight not greater than 500500 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 equal 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 500500 weights each of value 11. (b) How many different basic collections are there?
(D. Fomin, Leningrad)
combinatoricsweighings