Berit has 11 twenty-kroner , 14 ten-kroner and 12 five kroner coins
Source: Norwegian Mathematical Olympiad 2012 - Abel Competition p1a
September 4, 2019
number theoryalgebra
Problem Statement
Berit has twenty kroner coins, ten kroner coins, and five kroner coins. An exchange machine can exchange three ten kroner coins into one twenty kroner coin and two five kroner coins, and the reverse. It can also exchange two twenty kroner coins into three ten kroner coins and two five kroner coins, and the reverse.
(i) Can Berit get the same number of twenty kroner and ten kroner coins, but no five kroner coins?
(ii) Can she get the same number each of twenty kroner, ten kroner, and five kroner coins?