IMO 1978 Problem 6
- Day 2
An international society has its members from six different countries. The list of members contain names, numbered . Prove that there is at least one member whose number is the sum of the numbers of two members from his own country, or twice as large as the number of one member from his own country.
Official text Transcription from AI-MO AoPS, checked word for word against the official paper. Quoted with source.
Official text: IMO 1978 official English paper, page 1.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.