TOT 1998 Autumn OS5 intelligence quotient (IQ) of a country problem
Source:
May 11, 2020
combinatoricsAverage
Problem Statement
The intelligence quotient (IQ) of a country is defined as the average IQ of its entire population. It is assumed that the total population and individual IQs remain constant throughout.
(a) (i) A group of people from country has emigrated to country . Show that it can happen that as a result , the IQs of both countries have increased.
(ii) After this, a group of people from , which may include immigrants from , emigrates to . Can it happen that the IQs of both countries will increase again?
(b) A group of people from country has emigrated to country , and a group of people from has emigrated to country . It is known that a s a result , the IQs o f all three countries have increased. After this, a group of people from emigrates to and a group of people from emigrates to . Can it happen that the IQs of all three countries will increase again?(A Kanel, B Begun)