Vanya and Petya choosing numbers x and y...
Source: Tournament of towns, Junior A-Level paper, Fall 2004
December 25, 2004
geometrygeometric transformationalgebra unsolvedalgebra
Problem Statement
Vanya has chosen two positive numbers, x and y. He wrote the numbers x+y, x-y, x/y, and xy, and has shown these numbers to Petya. However, he didn't say which of the numbers was obtained from which operation. Show that Petya can uniquely recover x and y.