MathDB

250

Part of 1977 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 250 All Soviet Union MO 1977 scales and weights, in n-letter word

Source:

7/6/2019
Given scales and a set of nn different weights. We take weights in turn and add them on one of the scales sides. Let us denote "LL" the scales state with the left side down, and "RR" -- with the right side down.
a) Prove that you can arrange the weights in such an order, that we shall obtain the sequence LRLRLRLR...LRLRLRLR... of the scales states. (That means that the state of the scales will be changed after putting every new weight.)
b) Prove that for every nn-letter word containing RR's and LL's only you can arrange the weights in such an order, that the sequence of the scales states will be described by that word.
combinatoricsWords