DK-GEORGMOHR 2005 Problem 4
Fourteen students each write an integer number on the board. When they later meet their math teacher Homer Grog, they tell him that no matter what number they erased on the board, then the remaining numbers could be divided into three groups at once sum. They also tell him that the numbers on the board were integer numbers. Is it now possible for Homer Grog to determine what numbers the students wrote on the board?
Dataset text AI-MO AoPS. Quoted with source.
Official text: Georg Mohr Contest 2005 official 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.
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