# Asymmetric replacement

Start with the set $$\{2, 3, 4\}$$. In each step, choose two numbers $$a$$ and $$b$$, and replace them with $$0.6a-0.8b$$ and $$0.8a+0.6b$$.

(a) Is it possible to reach the set $$\{1, 3, 5\}$$?
(b) Is it possible to reach the set $$\{0, 2, 5\}$$?

(adapted from Engel, Problem Solving Strategies, p.9)

×